Convexity of the entropy of positive solutions to the heat equation on quaternionic contact and CR manifolds

Dimiter Vassilev

Vol. 289 (2017), No. 1, 189–201

DOI: 10.2140/pjm.2017.289.189

Abstract

A proof of the monotonicity of an entropy like energy for the heat equation on a quaternionic contact and CR manifolds is given.

Keywords

quaternionic contact structures, CR manifolds, entropy monotonicity, Paneitz operator, 3-Sasakian

Mathematical Subject Classification 2010

Primary: 32V05, 35H20, 35K05, 53C17, 53C25, 53C26, 53C21, 58J60, 35P15

Milestones

Received: 20 October 2016

Revised: 7 December 2016

Accepted: 12 December 2016

Published: 12 May 2017