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A partially overdetermined problem in domains with partial umbilical boundary in space forms.
- Source :
-
Advances in Calculus of Variations . Jan2024, Vol. 17 Issue 1, p11-31. 21p. - Publication Year :
- 2024
-
Abstract
- In the first part of this paper, we consider a partially overdetermined mixed boundary value problem in space forms and generalize the main result in [11] to the case of general domains with partial umbilical boundary in space forms. Precisely, we prove that a partially overdetermined problem in a domain with partial umbilical boundary admits a solution if and only if the rest part of the boundary is also part of an umbilical hypersurface. In the second part of this paper, we prove a Heintze–Karcher–Ros-type inequality for embedded hypersurfaces with free boundary lying on a horosphere or an equidistant hypersurface in the hyperbolic space. As an application, we show an Alexandrov-type theorem for constant mean curvature hypersurfaces with free boundary in these settings. [ABSTRACT FROM AUTHOR]
- Subjects :
- *BOUNDARY value problems
*HYPERSURFACES
*SUBMANIFOLDS
*CURVATURE
*HYPERBOLIC spaces
Subjects
Details
- Language :
- English
- ISSN :
- 18648258
- Volume :
- 17
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Advances in Calculus of Variations
- Publication Type :
- Academic Journal
- Accession number :
- 174631533
- Full Text :
- https://doi.org/10.1515/acv-2021-0090