Monotonicity and its analytic and geometric implications

By T. Colding, W. Minicozzi. Proceedings of the National Academy of Sciences of the United States of America, 2012

48 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/428bd43661ef51cab065734bfae333b8a4ec30b6

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In Applied Mathematics

1. Mattia Fogagnolo
2. L. Mazzieri
3. Virginia Agostiniani
4. Zoltán M. Balogh
5. Alexandru Krist'aly
6. M. Rigoli

Citations in the corpus

• Sharp geometric inequalities for closed hypersurfaces in manifolds with nonnegative Ricci curvature (2018, methodology): “n with the monotonicity formulas by Colding and Minicozzi In this section, we provide a comparison between our monotonicity formulas and those obtained by Colding and by Colding-Minicozzi in [21] and [24], respectively. To start with, let ube a solution of (1.9) in a nonparabolic Riemannian manifold”