Monotonicity - analytic and geometric implications
Differential Geometry
2012-06-11 v2 Analysis of PDEs
Abstract
In this expository article, we discuss various monotonicity formulas for parabolic and elliptic operators and explain how the analysis of the function spaces and the geometry of the underlining spaces are intertwined. After briefly discussing some of the well-known analytical applications of monotonicity for parabolic operators, we turn to their elliptic counterparts, their geometric meaning, and some geometric consequences.
Cite
@article{arxiv.1205.6768,
title = {Monotonicity - analytic and geometric implications},
author = {Tobias Holck Colding and William P. Minicozzi},
journal= {arXiv preprint arXiv:1205.6768},
year = {2012}
}