16 citations · 18 across the 4 of their papers we have counts for
6 papers
Moving monotonicity formulae for minimal submanifolds in constant curvature
Keaton Naff, Jonathan J. Zhu
We discover new monotonicity formulae for minimal submanifolds in space forms, which imply the sharp area bound for minimal submanifolds through a prescribed point in a geodesic ba…
Łojasiewicz inequalities for mean convex self-shrinkers
Jonathan J. Zhu
We prove Łojasiewicz inequalities for round cylinders and cylinders over Abresch-Langer curves, using perturbative analysis of a quantity introduced by Colding-Minicozzi. A feature…
Rigidity and Łojasiewicz inequalities for Clifford self-shrinkers
Ao Sun, Jonathan J. Zhu
We show that the product of two round shrinking spheres is an isolated self-shrinker in any codimension, modulo rotations. Moreover we prove explicit Łojasiewicz inequalities near…
Min-max theory for networks of constant geodesic curvature
Xin Zhou, Jonathan J. Zhu
We prove that on a closed surface, for any , our min-max theory for prescribing mean curvature produces a solution given by a curve of constant geodesic curvature which is…
Existence of hypersurfaces with prescribed mean curvature I - Generic min-max
Xin Zhou, Jonathan J. Zhu
We prove that, for a generic set of smooth prescription functions on a closed ambient manifold, there always exists a nontrivial, smooth, closed hypersurface of prescribed mean…
Min-max theory for constant mean curvature hypersurfaces
Xin Zhou, Jonathan J. Zhu
In this paper, we develop a min-max theory for the construction of constant mean curvature (CMC) hypersurfaces of prescribed mean curvature in an arbitrary closed manifold. As a co…