Monotonicity  analytic and geometric implications
Tobias Holck Colding, William P. Minicozzi II,
2012.05.30
http://arxiv.org/abs/1205.6768
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 wellknown analytical applications of
monotonicity for parabolic operators, we turn to their elliptic counterparts,
their geometric meaning, and some geometric consequences.
