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Creators/Authors contains: "Bernstein, Jacob"

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  1. ; (, Journal für die reine und angewandte Mathematik (Crelles Journal))
    Abstract We introduce a family of functionals defined on the set of submanifolds of Cartan–Hadamard manifolds which generalize the Colding–Minicozzi entropy of submanifolds of Euclidean space.We show 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. 
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    Free, publicly-accessible full text available May 3, 2026
  2. ; (, International Mathematics Research Notices)
    Abstract 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 with respect to the sphere’s standard CR-structure, we associate a quantity that is invariant under the CR-automorphisms of the sphere. We apply this concept to a corresponding notion of Willmore energy. 
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    Free, publicly-accessible full text available March 1, 2026
  3. ; (, Forum of Mathematics, Sigma)
    Abstract We prove lower bounds on the density of regular minimal cones of dimension less than seven provided the complements of the cones are topologically nontrivial. 
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  4. ; (, Notices of the American Mathematical Society)
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  5. ; (, Geometriae Dedicata)
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  6. (, Advanced Nonlinear Studies)
    Abstract 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 monotone along mean curvature flow. 
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  7. ; (, Peking Mathematical Journal)
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  8. ; (, Duke Mathematical Journal)
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  9. ; (, Advances in Mathematics)
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  10. ; (, Cambridge Journal of Mathematics)
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