Accès ouvert
2026
preprint
OpenAlex
Kahnrad Braxton, Tang-Kai Lee, Jonathan J. Zhu
We prove the linear stability of an embedded mean curvature flow shrinker in $\mathbb R^4$ with the topology of the Möbius bundle. This provides a non-flat, non-spherical stable shrinker in higher codimension, in sharp contrast with the classification of stable hypersurface shrinkers. …
Accès ouvert
2026
preprint
OpenAlex
Davide Parise, Jonathan J. Zhu
We prove that every smooth properly embedded free-boundary minimal annulus in the unit ball is congruent to the critical catenoid. We also classify positive solutions of $(Δ_{\mathbb{S}^2}+2)u=0$ on smooth spherical annuli with $u=0$ and $|\nabla u|=1$ on the boundary; their one-homogeneous extensions …
Accès ouvert
2026
preprint
OpenAlex
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 vertical line. We also show that the regular set of any entire, …
Accès ouvert
2026
preprint
OpenAlex
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 vertical line. We also show that the regular set of any entire, …
us
(code pays fourni par la source)
2026
article
OpenAlex
Jonathan J. Zhu, Keaton Naff
Accès ouvert
2025
preprint
OpenAlex
Jonathan J. Zhu
This is the second of two articles in which we investigate the geometry of free boundary and capillary minimal surfaces in balls $B_R\subset\mathbb{S}^3$. In this article, we find monotonicity formulae which imply that capillary minimal surfaces maximise a certain modified energy in …
Accès ouvert
2025
preprint
OpenAlex
Jonathan J. Zhu
This is the second of two articles in which we investigate the geometry of free boundary and capillary minimal surfaces in balls $B_R\subset\mathbb{S}^3$. In this article, we find monotonicity formulae which imply that capillary minimal surfaces maximise a certain modified energy in …
us
(code pays fourni par la source)
Accès ouvert
2025
preprint
OpenAlex
Keaton Naff, Jonathan J. Zhu
This is the first of two articles in which we investigate the geometry of free boundary and capillary minimal surfaces in balls $B_R\subset\mathbb{S}^3$. In this article, we extend our previous half-space intersection properties to warped products, and extend (non-)umbilicity of discs and …
2025
article
OpenAlex
Ao Sun, Jonathan J. Zhu
us
(code pays fourni par la source)
2025
article
OpenAlex
Keaton Naff, Jonathan J. Zhu
us
(code pays fourni par la source)
2025
article
OpenAlex
Sven Hirsch, Jonathan J. Zhu
Abstract We prove uniqueness of tangent cones for forced mean curvature flow, at both closed self-shrinkers and round cylindrical self-shrinkers, in any codimension. The corresponding results for mean curvature flow in Euclidean space were proven by Schulze and Colding–Minicozzi, respectively. We adapt …
us, fr
(code pays fourni par la source)
Accès ouvert
2025
article
OpenAlex
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, in any codimension. We deduce the uniqueness of blowups at singularities modelled on this class of cylinders, and …
us
(code pays fourni par la source)