Monotonicity and its analytic and geometric implications

In this expository article, we discuss various monotonicity formulas for parabolic and elliptic operators and explain how the analysis of function spaces and the geometry of the underlining spaces are intertwined. After briefly discussing some of the well-known analytical applications of monotonicit...

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Bibliographic Details
Main Authors: Colding, Tobias, Minicozzi, William
Other Authors: Massachusetts Institute of Technology. Department of Mathematics
Format: Article
Language:en_US
Published: National Academy of Sciences (U.S.) 2013
Online Access:http://hdl.handle.net/1721.1/77236
https://orcid.org/0000-0001-6208-384X
https://orcid.org/0000-0003-4211-6354