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Isoperimetric functional inequalities via the maximum principle: the exterior differential systems approach | | Paata Ivanisvili
; Alexander Volberg
; | | Date: |
21 Nov 2015 | | Abstract: | The goal of this note is to give the unified approach to the solutions of a
class of isoperimetric problems by relating them to the exterior differential
systems studied by R.~Bryant and P.~Griffiths. In this note we list several
classical by now isopereimetric inequalities which can be proved in a unified
way. This unified approach reduces them to the so-called exterior differential
systems studied by Robert Bryant and Phillip Griffiths. To the best of our
knowledge, this is the first article where this connection is used.
Key words: log-Sobolev inequality, Poincar’e inequality, Bobkov’s
inequality, Gaussian isoperimetry, semigroups, maximum principle,
Monge--Amp’ere equation with drift, exterior differential systems, backwards
heat equation, (B) theorem | | Source: | arXiv, 1511.6895 | | Services: | Forum | Review | PDF | Favorites | |
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