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Existence of monotone Morse flow lines of the expander functional
Jacob Bernstein, Letian Chen, Lu Wang
Given a smooth asymptotically conical self-expander that is strictly unstable we construct a (singular) Morse flow line of the expander functional that connects it to a stable self…
The CR-Volume of Horizontal Submanifolds of Spheres
Jacob Bernstein, Arunima Bhattacharya
We study an analog in CR-geometry of the conformal volume of Li-Yau. In particular, to submanifolds of odd-dimensional spheres that are Legendrian or, more generally, horizontal wi…
Minimal surfaces and Colding-Minicozzi entropy in complex hyperbolic space
Jacob Bernstein, Arunima Bhattacharya
We study notions of asymptotic regularity for a class of minimal submanifolds of complex hyperbolic space that includes minimal Lagrangian submanifolds. As an application, we show…
Hausdorff Stability of the Round Two-Sphere Under Small Perturbations of the Entropy
Jacob Bernstein, Lu Wang
We show that if a closed surface in has entropy near to that of the unit two-sphere, then the surface is close to a round two-sphere in the Hausdorff distance.