Monotonicity and its analytic and geometric implications

被引：23
作者：
Colding, Tobias Holck [1 ]
Minicozzi, William P., II [2 ]
机构：
[1] MIT, Cambridge, MA 02139 USA
[2] Johns Hopkins Univ, Baltimore, MD 21218 USA
来源：
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA | 2013年 / 110卷 / 48期
基金：
美国国家科学基金会;
关键词：
elliptic equations; parabolic equations; geometric inequalities; Ricci-flat; Einstein manifolds; RICCI CURVATURE; BOUNDS;
D O I：
10.1073/pnas.1203856109
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
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.
引用
收藏
页码：19233 / 19236
页数：4
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