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2,229 results on '"In-Ho Pak"'

1. Convergence rate of the $Q$-curvature flow

Author

Ho, Pak Tung and Lee, Sanghoon

Subjects
Mathematics - Differential Geometry, 53E99, 53C18, 35R01
Abstract

Carlotto, Chodosh and Rubinstein have studied the convergence rate of the Yamabe flow. Inspired by their result, we study the convergence rate of the $Q$-curvature flow in this paper. In particular, we provide an example of a slowly converging $Q_6$-curvature flow in dimension 6, in constrast to the dimension 2 case, where the $Q$-curvature flow always converges exponentially., Comment: All comments welcome! arXiv admin note: substantial text overlap with arXiv:2107.09616, arXiv:2212.04367; substantial text overlap with arXiv:1401.3738 by other authors

Published
2024

2. Deformations of the scalar curvature of a partially integrable pseudohermitian manifold

Author

Case, Jeffrey S. and Ho, Pak Tung

Subjects
Mathematics - Differential Geometry
Abstract

We consider deformations of the scalar curvature of a partially integrable pseudohermitian manifold, in analogy with the work of Fischer and Marsden on Riemannian manifolds. In particular, we introduce and discuss $R$-singular spaces, give sufficient conditions for the stability of the scalar curvature, and give a partial infinitesimal rigidity result for the scalar curvature of a compact, torsion-free, scalar-flat, integrable pseudohermitian manifold., Comment: 16 pages

Published
2024

5. Deformation of the Weighted Scalar Curvature

Author

Ho, Pak Tung and Shin, Jinwoo

Subjects
Mathematics - Differential Geometry
Abstract

Inspired by the work of Fischer-Marsden [Duke Math. J. 42 (1975), 519-547], we study in this paper the deformation of the weighted scalar curvature. By studying the kernel of the formal $L_\phi^2$-adjoint for the linearization of the weighted scalar curvature, we prove several geometric results. In particular, we define a weighted vacuum static space, and study locally conformally flat weighted vacuum static spaces. We then prove some stability results of the weighted scalar curvature on flat spaces. Finally, we consider the prescribed weighted scalar curvature problem on closed smooth metric measure spaces.

Published
2023
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7. The second Yamabe invariant with boundary

Author

Ho Pak Tung and Pyo Juncheol

Subjects
yamabe problem, yamabe flow, yamabe invariant, primary 53c18, secondary 53c21, 35r01, 53e99, Analysis, QA299.6-433
Abstract

Let (M,∂M,g)\left(M,\partial M,g) be a compact Riemannian manifold with boundary. As a generalization of the Yamabe invariant with boundary Y(M,∂M,g)Y\left(M,\partial M,g), we define the kth Yamabe invariant with boundary Yk(M,∂M,g){Y}_{k}\left(M,\partial M,g). We prove some of its properties and study when it can be attained by the generalized metric. We also prove a version of conformal Schwarz lemma on (M,∂M,g)\left(M,\partial M,g) by using the Yamabe flow with boundary.

Published
2024
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8. Convergence rate of the weighted Yamabe flow

Author

Ho, Pak Tung, Shin, Jinwoo, and Yan, Zetian

Subjects
Mathematics - Differential Geometry, 53E99
Abstract

The weighted Yamabe flow was the geometric flow introduced to study the weighted Yamabe problem on smooth metric measure spaces. Carlotto, Chodosh and Rubinstein have studied the convergence rate of the Yamabe flow. Inspired by their result, we study in this paper the convergence rate of the weighted Yamabe flow., Comment: arXiv admin note: substantial text overlap with arXiv:2107.09616. substantial text overlap with arXiv:1401.3738 by other authors

Published
2022

9. Some results on the weighted Yamabe problem with or without boundary

Author

Ho, Pak Tung, Shin, Jinwoo, and Yan, Zetian

Subjects
Mathematics - Differential Geometry
Abstract

Let $(M^n,g,e^{-\phi}dV_g,e^{-\phi}dA_g,m)$ be a compact smooth metric measure space with boundary with $n\geqslant 3$. In this article, we consider several Yamabe-type problems on a compact smooth metric measure space with or without boundary: uniqueness problem on the weighted Yamabe problem with boundary, characterization of the weighted Yamabe solitons with boundary and the existence of positive minimizers in the weighted Escobar quotient.

Published
2022

11. The weighted Yamabe problem with boundary

Author

Ho, Pak Tung, Shin, Jinwoo, and Yan, Zetian

Subjects
Mathematics - Differential Geometry
Abstract

We introduce a Yamabe-type flow \begin{align*} \left\{ \begin{array}{ll} \frac{\partial g}{\partial t} &=(r^m_{\phi}-R^m_{\phi})g \\ \frac{\partial \phi}{\partial t} &=\frac{m}{2}(R^m_{\phi}-r^m_{\phi}) \end{array} \right. ~~\mbox{ in }M ~~\mbox{ and }~~ H^m_{\phi}=0 ~~\mbox{ on }\partial M \end{align*} on a smooth metric measure space with boundary $(M,g, v^mdV_g,v^mdA_g,m)$, where $R^m_{\phi}$ is the associated weighted scalar curvature, $r^m_{\phi}$ is the average of the weighted scalar curvature, and $H^m_{\phi}$ is the weighted mean curvature. We prove the long-time existence and convergence of this flow.

Published
2022

12. Global impact of 10- and 13-valent pneumococcal conjugate vaccines on pneumococcal meningitis in all ages: The PSERENADE project

Author

Yang, Yangyupei, Knoll, Maria Deloria, Herbert, Carly, Bennett, Julia C., Feikin, Daniel R., Garcia Quesada, Maria, Hetrich, Marissa K., Zeger, Scott L., Kagucia, Eunice W., Xiao, Melody, Cohen, Adam L., van der Linden, Mark, du Plessis, Mignon, Yildirim, Inci, Winje, Brita A., Varon, Emmanuelle, Valenzuela, Maria Teresa, Valentiner-Branth, Palle, Steens, Anneke, Scott, J. Anthony, Savrasova, Larisa, Sanz, Juan Carlos, Khan, Aalisha Sahu, Oishi, Kazunori, Nzoyikorera, Néhémie, Nuorti, J. Pekka, Mereckiene, Jolita, McMahon, Kimberley, McGeer, Allison, Mackenzie, Grant A., MacDonald, Laura, Ladhani, Shamez N., Kristinsson, Karl G., Kleynhans, Jackie, Kellner, James D., Jayasinghe, Sanjay, Ho, Pak-Leung, Hilty, Markus, Hammitt, Laura L., Guevara, Marcela, Gilkison, Charlotte, Gierke, Ryan, Desmet, Stefanie, De Wals, Philippe, Dagan, Ron, Colzani, Edoardo, Ciruela, Pilar, Chuluunbat, Urtnasan, Chan, Guanhao, Camilli, Romina, Bruce, Michael G., Brandileone, Maria-Cristina C., Ampofo, Krow, O’Brien, Katherine L., and Hayford, Kyla

Published
2025
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13. The crosstalk between cholangiocytes and hepatic stellate cells promotes the progression of epithelial-mesenchymal transition and periductal fibrosis during Clonorchis sinensis infection

Author

Junyeong Yi, Ji Hoon Jeong, Jihee Won, Seok Chung, and Jhang Ho Pak

Subjects
Clonorchis sinensis, Excretory-secretory products, Cholangiocytes, Hepatic stellate cells, Intercellular crosstalk, Epithelial-mesenchymal transition, Infectious and parasitic diseases, RC109-216
Abstract

A bstract Background Clonorchis sinensis infection is one of the risk factors that provokes chronic inflammation, epithelial hyperplasia, periductal fibrosis and even cholangiocarcinoma (CCA). Disrupted or aberrant intercellular communication among liver-constituting cells leads to pathological states that cause various hepatic diseases. This study was designed to investigate the pathological changes caused by C. sinensis excretory-secretory products (ESPs) in non-cancerous human cell lines (cholangiocytes [H69 cell line] and human hepatic stellate cells [LX2 cell line]) and their intercellular crosstalk, as well the pathological changes in infected mouse liver tissues. Methods The cells were treated with ESPs, following which transforming growth factor beta 1 (TGF-β1) and interleukin-6 (IL-6) secretion levels and epithelial-mesenchymal transition (EMT)- and fibrosis-related protein expression were measured. The ESP-mediated cellular motility (migration/invasion) between two cells was assessed using the Transwell and three-dimensional microfluidic assay models. The livers of C. sinensis-infected mice were stained using EMT and fibrotic marker proteins. Results Treatment of cells with ESPs increased TGF-β1 and IL-6 secretion and the expression of EMT- and fibrosis-related proteins. The ESP-mediated mutual cell interaction further affected the cytokine secretion and protein expression levels and promoted cellular motility. N-cadherin overexpression and collagen fiber deposition were observed in the livers of C. sinensis-infected mice. Conclusions These findings suggest that EMT and biliary fibrosis occur through intercellular communication between cholangiocytes and hepatic stellate cells during C. sinensis infection, promoting malignant transformation and advanced hepatobiliary abnormalities. Graphical Abstract

Published
2024
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18. Convergence rate of the prescribed curvature flow

Author

Ho, Pak Tung and Shin, Jinwoo

Subjects
Mathematics - Differential Geometry
Abstract

The prescribed scalar curvature flow was introduced to study the problem of prescribing scalar curvature on manifolds. Carlotto, Chodosh and Rubinstein have studied the convergence rate of the Yamabe flow. Inspired by their result, we study in this paper the convergence rate of the prescribed scalar curvature flow., Comment: Example in section 5 is not correct

Published
2021

19. Prescribed Webster scalar curvature flow on CR manifold

Author

Ho, Pak Tung, Ngo, Quoc Anh, and Zhang, Hong

Subjects
Mathematics - Differential Geometry, Mathematics - Complex Variables
Abstract

Using the prescribed Webster scalar curvature flow, we prove some existence results on the 3-dimensional compact CR manifold with nonnegative CR Yamabe constant.

Published
2021

25. Deformation of the scalar curvature and the mean curvature

Author

Ho, Pak Tung and Huang, Yen-Chang

Subjects
Mathematics - Differential Geometry, 53C20, 53C21
Abstract

On a compact manifold $M$ with boundary $\partial M$, we study the problem of prescribing the scalar curvature in $M$ and the mean curvature on the boundary $\partial M$ simultaneously. To do this, we introduce the notion of singular metric, which is inspired by the early work of Fischer-Marsden in [18] and Lin-Yuan in [23] for closed manifold. We show that we can prescribe the scalar curvature and the mean curvature simultaneously for generic scalar-flat manifolds with minimal boundary. We also prove some rigidity results for the flat manifolds with totally geodesic boundary., Comment: 15 pages

Published
2020

26. CR Yamabe constant, CR Yamabe flow and its soliton

Author

Ho, Pak Tung and Wang, Kunbo

Subjects
Mathematics - Differential Geometry, 32V05, 32V20, 53C44
Abstract

On a compact strictly pseudoconvex CR manifold $(M,\th)$, we consider the CR Yamabe constant of its infinite conformal covering. By using the maximum principles, we then prove a uniqueness theorem for the CR Yamabe flow on a complete noncompact CR manifold. Finally we obtain some properties of the CR Yamabe soliton on complete noncompact CR manifolds., Comment: To appear in NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS

Published
2020

31. Global impact of ten-valent and 13-valent pneumococcal conjugate vaccines on invasive pneumococcal disease in all ages (the PSERENADE project): a global surveillance analysis

Author

Pennington, Kate, Krause, Vicki, Rahman, Hafizur, Almeida, Samanta, Kellner, James, Deceuninck, Geneviève, Lefebvre, Brigitte, Hormazabal, Juan, Valenzuela, Maria Teresa, Krizova, Pavla, Sahu Khan, Aalisha, Toropainen, Maija, Varon, Emmanuelle, Ploy, Marie-Cecile, Hossain, Ilias, Magaziotou, Ioanna, Tzanakaki, Georgina, Chow, Kin-Hung, Erlendsdottir, Helga, Corcoran, Mary, Riccardo, Flavia, Oishi, Kazunori, Verani, Jennifer, Dimina, Elina, Swarthout, Todd, Mungun, Tuya, Zerouali, Khalid, van Sorge, Nina, Gilkison, Charlotte, Vestrheim, Didrik, Kuch, Alicja, Thoon, Koh Cheng, Ang, Michelle, Avdičová, Mária, Kleynhans, Jackie, de Gouveia, Linda, Muñoz-Almagro, Carmen, de Miguel, Sara, Castilla, Jesús, Morfeldt, Eva, Amin-Chowdhury, Zahin, Smith, Andrew, Pilishvili, Tamara, Kobayashi, Miwako, Reasonover, Alisa, Pelton, Stephen, Sutcliffe, Catherine, Aukes, Laurie, Byington, Carrie, Dalby, Tine, Celentano, Lucia, Hanquet, Germaine, Bennett, Julia C, Deloria Knoll, Maria, Kagucia, Eunice W, Garcia Quesada, Maria, Zeger, Scott L, Hetrich, Marissa K, Yang, Yangyupei, Herbert, Carly, Ogyu, Anju, Cohen, Adam L, Yildirim, Inci, Winje, Brita A, von Gottberg, Anne, Viriot, Delphine, van der Linden, Mark, Valentiner-Branth, Palle, Suga, Shigeru, Steens, Anneke, Skoczynska, Anna, Sinkovec Zorko, Nadja, Scott, J Anthony, Savulescu, Camelia, Savrasova, Larisa, Sanz, Juan Carlos, Russell, Fiona, Ricketson, Leah J, Puentes, Rodrigo, Nuorti, J Pekka, Mereckiene, Jolita, McMahon, Kimberley, McGeer, Allison, Mad'arová, Lucia, Mackenzie, Grant A, MacDonald, Laura, Lepp, Tiia, Ladhani, Shamez N, Kristinsson, Karl G, Kozakova, Jana, Klein, Nicola P, Jayasinghe, Sanjay, Ho, Pak-Leung, Hilty, Markus, Heyderman, Robert S, Hasanuzzaman, Md, Hammitt, Laura L, Guevara, Marcela, Grgic-Vitek, Marta, Gierke, Ryan, Georgakopoulou, Theano, Galloway, Yvonne, Diawara, Idrissa, Desmet, Stefanie, De Wals, Philippe, Dagan, Ron, Colzani, Edoardo, Cohen, Cheryl, Ciruela, Pilar, Chuluunbat, Urtnasan, Chan, Guanhao, Camilli, Romina, Bruce, Michael G, Brandileone, Maria-Cristina C, Bigogo, Godfrey, Ampofo, Krow, O'Brien, Katherine L, Feikin, Daniel R, and Hayford, Kyla

Published
2024
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32. Serotype distribution of remaining invasive pneumococcal disease after extensive use of ten-valent and 13-valent pneumococcal conjugate vaccines (the PSERENADE project): a global surveillance analysis

Author

Pennington, Kate, Krause, Vicki, Brandileone, Maria-Cristina, Ricketson, Leah, Deceuninck, Geneviève, Lefebvre, Brigitte, Díaz, Janepsy, Puentes, Rodrigo, Krizova, Pavla, Rafai, Eric, Toropainen, Maija, Viriot, Delphine, Ploy, Marie-Cecile, Hossain, Ilias, Georgakopoulou, Theano, Magaziotou, Ioanna, Chow, Kin-Hung, Erlendsdottir, Helga, Mereckiene, Jolita, Del Manso, Martina, Suga, Shigeru, Bigogo, Godfrey, Dimina, Elina, Swarthout, Todd, Nzoyikorera, Néhémie, Steens, Anneke, Galloway, Yvonne, Winje, Brita, Chan, Guanhao, Thoon, Koh Cheng, Avdičová, Mária, de Gouveia, Linda, du Plessis, Mignon, Ciruela, Pilar, Sanz, Juan Carlos, Guevara, Marcela, Lepp, Tiia, Amin-Chowdhury, Zahin, Macdonald, Laura, Pilishvili, Tamara, Kobayashi, Miwako, Bruden, Dana, Pelton, Stephen, Sutcliffe, Catherine, Aukes, Laurie, Byington, Carrie, Zintgraff, Jonathan, Chamorro, Gustavo, Kawabata, Aníbal, Celentano, Lucia, Rey-Benito, Gloria, Nakamura, Tomoka, Garcia Quesada, Maria, Peterson, Meagan E, Bennett, Julia C, Hayford, Kyla, Zeger, Scott L, Yang, Yangyupei, Hetrich, Marissa K, Feikin, Daniel R, Cohen, Adam L, von Gottberg, Anne, van der Linden, Mark, van Sorge, Nina M, de Oliveira, Lucia H, de Miguel, Sara, Yildirim, Inci, Vestrheim, Didrik F, Verani, Jennifer R, Varon, Emmanuelle, Valentiner-Branth, Palle, Tzanakaki, Georgina, Sinkovec Zorko, Nadja, Setchanova, Lena P, Serhan, Fatima, Scott, Kevin J, Scott, J Anthony, Savulescu, Camelia, Savrasova, Larisa, Reyburn, Rita, Oishi, Kazunori, Nuorti, J Pekka, Napoli, Daniela, Mwenda, Jason M, Muñoz-Almagro, Carmen, Morfeldt, Eva, McMahon, Kimberley, McGeer, Allison, Mad'arová, Lucia, Mackenzie, Grant A, Eugenia León, Maria, Ladhani, Shamez N, Kristinsson, Karl G, Kozakova, Jana, Kleynhans, Jackie, Klein, Nicola P, Kellner, James D, Jayasinghe, Sanjay, Ho, Pak-Leung, Hilty, Markus, Harker-Jones, Marcella A, Hammitt, Laura L, Grgic-Vitek, Marta, Gilkison, Charlotte, Gierke, Ryan, French, Neil, Diawara, Idrissa, Desmet, Stefanie, De Wals, Philippe, Dalby, Tine, Dagan, Ron, Corcoran, Mary, Colzani, Edoardo, Chanto Chacón, Grettel, Castilla, Jesús, Camilli, Romina, Ang, Michelle, Ampofo, Krow, Almeida, Samanta C G, Alarcon, Pedro, O'Brien, Katherine L, and Deloria Knoll, Maria

Published
2024
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36. A fractional conformal curvature flow on the unit sphere

Author

Chen, Xuezhang and Ho, Pak Tung

Subjects
Mathematics - Differential Geometry, Mathematics - Analysis of PDEs
Abstract

We study a fractional conformal curvature flow on the standard unit sphere and prove a perturbation result of the fractional Nirenberg problem with fractional exponent $\sigma \in (1/2,1)$. This extends the result of Chen-Xu (Invent. Math. 187, no. 2, 395-506, 2012) for the scalar curvature flow on the standard unit sphere., Comment: An intermediate version, still needs to be updated

Published
2019

42. Connected sum of CR manifolds with positive CR Yamabe constant

Author

Cheng, Jih-Hsin, Chiu, Hung-Lin, and Ho, Pak Tung

Subjects
Mathematics - Differential Geometry, 32V99, 32V20
Abstract

Suppose $M_{1}$ and $M_{2}$ are $3$-dimensional closed (compact without boundary) CR manifolds with positive CR Yamabe constant. In this note, we show that the connected sum of $M_{1}$ and $M_{2}$ also admits a CR structure with positive CR Yamabe constant.

Published
2019
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