17 citations · 73 across the 17 of their papers we have counts for
21 papers · 1 filter
A stable self-shrinking Möbius bundle in
Kahnrad Braxton, Tang-Kai Lee, Jonathan J. Zhu
We prove the linear stability of an embedded mean curvature flow shrinker in with the topology of the Möbius bundle. This provides a non-flat, non-spherical stable sh…
A Bernstein-type theorem for capillary graphs in a half-space
Nick Edelen, Chao Li, Jonathan J. Zhu
We show that any entire, capillary minimal graph in a half-space must be linear in low-dimensions or, more generally, when some tangent cone at infinity does not split off a vertic…
A distance comparison principle for curve shortening flow with free boundary
Mat Langford, Jonathan J. Zhu
We introduce a reflected chord-arc profile for curves with orthogonal boundary condition and obtain a chord-arc estimate for embedded free boundary curve shortening flows in a conv…
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…
The prescribed point area estimate for minimal submanifolds in constant curvature
Keaton Naff, Jonathan J. Zhu
We prove a sharp area estimate for minimal submanifolds that pass through a prescribed point in a geodesic ball in hyperbolic space, in any dimension and codimension. In certain ca…
Widths of balls and free boundary minimal submanifolds
Jonathan J. Zhu
We observe that the -dimensional width of an -ball in a space form is given by the area of an equatorial -ball. We also investigate related lower bounds for the area of a…
Min-max theory for capillary surfaces
Chao Li, Xin Zhou, Jonathan J. Zhu
We develop a min-max theory for the construction of capillary surfaces in 3-manifolds with smooth boundary. In particular, for a generic set of ambient metrics, we prove the existe…
Rigidity of spherical product Ricci solitons
Ao Sun, Jonathan J. Zhu
We show that is isolated as a shrinking Ricci soliton in the space of metrics, up to scaling and diffeomorphism. We also prove the same rigidity for ,…
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…
Łojasiewicz inequalities, uniqueness and rigidity for cylindrical self-shrinkers
Jonathan J. Zhu
We establish Łojasiewicz inequalities for a class of cylindrical self-shrinkers for the mean curvature flow, which includes round cylinders and cylinders over Abresch-Langer curves…
Mean convex mean curvature flow with free boundary
Nick Edelen, Robert Haslhofer, Mohammad N. Ivaki +1
In this paper, we generalize White's regularity and structure theory for mean-convex mean curvature flow to the setting with free boundary. A major new challenge in the free bounda…
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…
Moving-centre monotonicity formulae for minimal submanifolds and related equations
Jonathan J. Zhu
Monotonicity formulae play a crucial role for many geometric PDEs, especially for their regularity theories. For minimal submanifolds in a Euclidean ball, the classical monotonicit…
First stability eigenvalue of singular minimal hypersurfaces in spheres
Jonathan J. Zhu
In this short note we extend an estimate due to J. Simons on the first stability eigenvalue of minimal hypersurfaces in spheres to the singular setting. Specifically, we show that…
On the entropy of closed hypersurfaces and singular self-shrinkers
Jonathan J. Zhu
Self-shrinkers are the special solutions of mean curvature flow in that evolve by shrinking homothetically; they serve as singularity models for the flow. The en…
On the rigidity of mean convex self-shrinkers
Qiang Guang, Jonathan J. Zhu
Self-shrinkers model singularities of the mean curvature flow; they are defined as the special solutions that contract homothetically under the flow. Colding-Ilmanen-Minicozzi show…
Minimal hypersurfaces with small first eigenvalue in manifolds of positive Ricci curvature
Jonathan J. Zhu
In this paper we exhibit deformations of the hemisphere , , for which the ambient Ricci curvature lower bound and the minimality of the boun…
Rigidity and Curvature Estimates for Graphical Self-shrinkers
Qiang Guang, Jonathan J. Zhu
Self-shrinkers are hypersurfaces that shrink homothetically under mean curvature flow; these solitons model the singularities of the flow. It it presently known that an entire self…