7 papers
Willmore energy and minimal fillings
Jacob Bernstein, Daniel Ketover
For each , we show that the infimal Willmore energy of a non-orientable surface of odd genus immersed in is attained by an index minimal surface in…
Minimal equatorial fillings of low index
Jacob Bernstein, Daniel Ketover
We obtain restrictions on the geometry and topology of minimal equatorial fillings in of the lowest possible Morse index.
On the Willmore energy of Möbius bands
Jacob Bernstein, Daniel Ketover
We show that among Möbius bands in bounded by a great circle, the minimal Willmore energy is realized by an embedded minimal Möbius band with Morse index two. To pro…
Minimal equatorial fillings
Jacob Bernstein, Daniel Ketover
We show that a great circle in bounds embedded non-orientable minimal surfaces of unbounded genera and all possible non-zero Euler numbers. This answers a question o…
Orientable minimal submanifolds of low index in the sphere
Jacob Bernstein, Daniel Ketover
In this short note we prove a rigidity result for orientable minimal submanifolds in the round sphere of the lowest non-trivial Morse index. In particular, we show that the only cl…
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…