Monotonicity and its analytic and geometric implications

Author(s)
Colding, Tobias; Minicozzi, William
Thumbnail
DownloadColding-2012-Monotonicity and its analytic and geometric implications.pdf (506.8Kb)
PUBLISHER_CC
Terms of use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Metadata
Show full item record
Abstract
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 monotonicity for parabolic operators, we turn to their elliptic counterparts, their geometric meaning, and some geometric consequences.
Date issued
2012-08
URI
http://hdl.handle.net/1721.1/77236
Department
Massachusetts Institute of Technology. Department of Mathematics
Journal
Proceedings of the National Academy of Sciences of the United States of America
Publisher
National Academy of Sciences (U.S.)
Citation
Colding, T. H., and W. P. Minicozzi. “Monotonicity and Its Analytic and Geometric Implications.” Proceedings of the National Academy of Sciences (2012).
Version: Final published version
ISSN
0027-8424
1091-6490
Collections