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46 results on '"Lin, Youjiang"'

2. The Petty projection inequality for sets of finite perimeter

Author

Lin, Youjiang

Subjects
Mathematics - Functional Analysis, Mathematics - Metric Geometry
Abstract

The Petty projection inequality for sets of finite perimeter is proved. Our approach is based on Steiner symmetrization. Neither the affine Sobolev inequality nor the functional Minkowski problem is used in our proof. Moreover, for sets of finite perimeter, we prove the Petty projection inequality with respect to Steiner symmetrization.

Published
2021

3. Affine Orlicz P\'olya-Szeg\'o principles and their equality cases

Author

Lin, Youjiang and Xi, Dongmeng

Subjects
Mathematics - Metric Geometry, 46E35, 46E30, 52A40
Abstract

The conjecture about the Orlicz P\'olya-Szeg\"o principle posed in [43] is proved. The cases of equality are characterized in the affine Orlicz P\'olya-Szeg\"o principle with respect to Steiner symmetrization and Schwarz spherical symmetrization.

Published
2020

6. An affine Orlicz Polya-Szego principle

Author

Lin, Youjiang

Subjects
Mathematics - Functional Analysis
Abstract

The author established the affine Orlicz Polya-Szego principle for log-concave functions and conjectured that the principle can be extended to the general Orlicz Sobolev functions. In this paper, we confirm this conjecture completely. An affine Orlicz Polya-Szego principle, which includes all the previous affine Polya-Szego principles as special cases, is formulated and proved. As a consequence, an Orlicz-Petty projection inequality for star bodies is established.

Published
2017

9. On the Gaussian Projection Inequalities.

Author

Lin, Youjiang and Xing, Sudan

Subjects
*FUNCTIONS of bounded variation
Abstract

We provide an overview of projection bodies in Gaussian probability space for sets of finite Gaussian perimeter and their corresponding applications in functions of Bounded variation space. On the one hand, we study the properties of Gaussian projection bodies for sets of finite Gaussian perimeter under Ehrhard symmetrization and establish a Gaussian projection-type inequality. This inequality concludes that Ehrhard symmetrization contracts the Minkowski symmetrization of the Gaussian projection body for set of finite Gaussian perimeter |$E$|⁠. On the other hand, we investigate the functional "lifting" of Ehrhard symmetrization and establish the affine Gaussian Pólya–Szegö-type inequalities in terms of the functional Ehrhard symmetrization. [ABSTRACT FROM AUTHOR]

Published
2024
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10. Some inequalities for star duality of the radial Blaschke-Minkowski homomorphisms

Author

Zhao Xia, Wang Weidong, and Lin Youjiang

Subjects
radial blaschke-minkowski homomorphism, star duality, brunn-minkowski inequality, monotonic inequality, shephard-type problem, dual quermassintegral, 52a20, 52a39, 52a40, Mathematics, QA1-939
Abstract

In 2006, Schuster introduced the radial Blaschke-Minkowski homomorphisms. In this article, associating with the star duality of star bodies and dual quermassintegrals, we establish Brunn-Minkowski inequalities and monotonic inequality for the radial Blaschke-Minkowski homomorphisms. In addition, we consider its Shephard-type problems and give a positive form and a negative answer, respectively.

Published
2020
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12. Origin-Symmetric Bodies of Revolution with Minimal Mahler Volume in R^3-a new proof

Author

Lin, Youjiang and Leng, Gangsong

Subjects
Mathematics - Differential Geometry
Abstract

Meyer and Reisner had proved the Mahler conjecture for rovelution bodies. In this paper, using a new method, we prove that among origin-symmetric bodies of revolution in R^3, cylinders have the minimal Mahler volume. Further, we prove that among parallel sections homothety bodies in R^3, 3-cubes have the minimal Mahler volume.

Published
2014

13. A new approach to Steiner symmetrization of coercive convex functions

Author

Lin, Youjiang, Leng, Gangsong, and Guo, Lujun

Subjects
Mathematics - Differential Geometry
Abstract

In this paper, a new approach of defining Steiner symmetrization of coercive convex functions is proposed and some fundamental properties of the new Steiner symmetrization are proved. Further, using the new Steiner symmetrization, we give a different approach to prove a functional version of the Blaschke-Santalo inequality due to Ball.

Published
2014

14. On the functional Blaschke-Santalo inequality

Author

Lin, Youjiang and Leng, Gangsong

Subjects
Mathematics - Differential Geometry, Mathematics - Functional Analysis, 52A10 52A40
Abstract

In this paper, using functional Steiner symmetrizations, we show that Meyer and Pajor's proof of the Blaschke-Santalo inequality can be extended to the functional setting., Comment: 14pages, 19conferences

Published
2014

15. Convex Bodies With Minimal Volume Product in R^2 --- A New Proof

Author

Lin, Youjiang

Subjects
Mathematics - Metric Geometry, 52A10, 52A40
Abstract

In this paper, a new proof of the following result is given: The product of the volumes of an origin symmetric convex bodies $K$ in R^2 and of its polar body is minimal if and only if $K$ is a parallelogram., Comment: 14pages, 4 figures, 14 conferences

Published
2010

20. The Non-Convergence of Steiner Symmetrizations.

Author

WANG Tian and LIN Youjiang

Abstract

In this paper, we demonstrate the existence of iterated Steiner symmetrizations of K that does not converge, even if the sequence of directions is dense in the unit sphere. [ABSTRACT FROM AUTHOR]

Published
2023
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31. Affine Orlicz Pólya–Szegö Principles and Their Equality Cases.

Author

Lin, Youjiang and Xi, Dongmeng

Subjects
*LOGICAL prediction
Abstract

The conjecture about the Orlicz Pólya–Szegö principle posed in [ 42 ] is proved. The cases of equality are characterized in the affine Orlicz Pólya–Szegö principle with respect to Steiner symmetrization and Schwarz spherical symmetrization. [ABSTRACT FROM AUTHOR]

Published
2021
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35. Mixed complex brightness integrals.

Author

Li, Chao, Wang, Weidong, and Lin, Youjiang

Subjects
INTEGRALS, MATHEMATICAL equivalence, INTEGRAL inequalities
Abstract

The notion of the mixed brightness was first introduced by Lutwak. Recently, Abardia and Bernig presented complex projection bodies. Based on this notion, we define the mixed complex brightness integrals and establish related Aleksandrov–Fenchel inequality, cyclic inequality and monotonicity inequality, respectively. [ABSTRACT FROM AUTHOR]

Published
2020
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46. Convex bodies with minimal volume product in R2 — a new proof

Author

Lin, Youjiang and Leng, Gangsong

Subjects
Mahler conjecture, Convex body, Polytope, Polar body
Abstract

A new proof of the Mahler conjecture in R2 is given. In order to prove the result, we introduce a new method — the vertex removal method; i.e., for any origin-symmetric polygon P, there exists a linear image ϕP contained in the unit disk B2, and there exist three contiguous vertices of ϕP lying on the boundary of B2. We can show that the volume-product of P decreases when we remove the middle vertex of the three vertices.

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