Integral Formulas for a Class of Curvature PDE'S and Application to Isoperimetric Inequalities and to Symmetry Problems

Martino, Vittorio ; Montanari, Annamaria (2008) Integral Formulas for a Class of Curvature PDE'S and Application to Isoperimetric Inequalities and to Symmetry Problems. [Preprint]
Full text available as:
[img]
Preview
PDF
License: Creative Commons Attribution Non-commercial

Download (196kB) | Preview

Abstract

We prove integral formulas for closed hypersurfaces in C^(n+1); which furnish a relation between elementary symmetric functions in the eigenvalues of the complex Hessian matrix of the defining function and the Levi curvatures of the hypersurface. Then we follow the Reilly approach to prove an isoperimetric inequality. As an application, we obtain the "Soap Bubble Theorem" for star- shaped domains with positive and constant Levi curvatures bounding the classical mean curvature from above.

Abstract
Document type
Preprint
Creators
CreatorsAffiliationORCID
Martino, Vittorio
Montanari, Annamaria
Keywords
isoperimetric inequality, Levi curvatures
Subjects
DOI
Deposit date
18 Mar 2008
Last modified
06 May 2015 07:40
URI

Other metadata

Downloads

Downloads

Staff only: View the document

^