Monotonicity and its analytic and geometric implications
Name
Colding-2012-Monotonicity and its analytic and geometric implications.pdf
Size
506.81 KB
Format
Adobe PDF
Checksum (MD5)
bcfba536c75cb7454d0f0bd73c05ca98
Author(s)
Colding, Tobias
Minicozzi, William
Date Issued
August 2012
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
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1073/pnas.1203856109
