54 citations · 160 across the 29 of their papers we have counts for
32 papers
Rigidity Properties of Colding-Minicozzi Entropies
Jacob Bernstein
We show certain rigidity for minimizers of generalized Colding-Minicozzi entropies. The proofs are elementary and work even in situations where the generalized entropies are not mo…
Colding-Minicozzi Entropies in Cartan-Hadamard Manifolds
Jacob Bernstein, Arunima Bhattacharya
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 the…
A Sharp Isoperimetric Property of the Renormalized Area of a Minimal Surface in Hyperbolic Space
Jacob Bernstein
We prove an inequality bounding the renormalized area of a complete minimal surface in hyperbolic space in terms of the conformal length of its ideal boundary.
Colding Minicozzi Entropy in Hyperbolic Space
Jacob Bernstein
This note introduces a notion of entropy for submanifolds of hyperbolic space analogous to the one introduced by Colding and Minicozzi for submanifolds of Euclidean space. Several…
Closed hypersurfaces of low entropy in are isotopically trivial
Jacob Bernstein, Lu Wang
We show that any closed connected hypersurface in with entropy less than or equal to that of the round cylinder is smoothly isotopic to the standard three-sphere.
A mountain-pass theorem for asymptotically conical self-expanders
Jacob Bernstein, Lu Wang
We develop a min-max theory for asymptotically conical self-expanders of mean curvature flow. In particular, we show that given two distinct strictly stable self-expanders that are…