As on arXiv
Abstract
We introduce a family of functionals on submanifolds of Cartan-Hadamard manifolds that generalize the Colding-Minicozzi entropy of submanifolds of Euclidean space. We show that these functionals are monotone under mean curvature flow under natural conditions. As a consequence, we obtain sharp lower bounds on these entropies for certain closed hypersurfaces and observe a novel rigidity phenomenon.
Comments: 34 pages
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Connected papers
The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2021, plus the canon.
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Rigidity Properties of Colding-Minicozzi Entropies
Topics Stability & uniqueness · Same author Jacob Bernstein · Shared terms “Minicozzi entropy”, “Colding Minicozzi”, “monotone”
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Li-Yau Conformal Volume and Colding-Minicozzi Entropy of Self-Shrinkers
Topics Mean curvature flow · Same author Jacob Bernstein · Shared terms “Minicozzi entropy”, “Colding Minicozzi”, “Euclidean space”
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Mean curvature flow of graphs with asymptotic Dirichlet conditions in Cartan-Hadamard manifolds
Topics Mean curvature flow · Shared terms “Cartan Hadamard”, “Hadamard manifolds”
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Minkowski inequality in Cartan-Hadamard manifolds
Topics Mean curvature flow · Shared terms “Cartan Hadamard”, “Hadamard manifolds”, “lower bound”
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Cylindrical tangent flows in mean curvature flow
Topics Stability & uniqueness · Shared terms “Colding Minicozzi”
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Sharp Minkowski-Type Inequality in Cartan-Hadamard 3-Spaces
Topics Mean curvature flow · Shared terms “Cartan Hadamard”
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Optimal Transport and Generalized Lagrangian Mean Curvature Flows on Kim-McCann Metrics
Topics Mean curvature flow · Same author Arunima Bhattacharya · Shared terms “submanifolds”
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Uniqueness of blowups for forced mean curvature flow
Topics Stability & uniqueness · Shared terms “Colding Minicozzi”, “Euclidean space”
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In the guidebook
- 6A.10Curve Shortening and the First Geometric Flows
Shrinking circles, grim reapers, neckpinches and Huisken’s monotonicity, seen in the plane.