Author

Jonathan J. Zhu

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Preprint Sep 2026

A stable self-shrinking M\"{o}bius bundle in $\mathbb R^4$

We prove the linear stability of an embedded mean curvature flow shrinker in $\mathbb R^4$ with the topology of the M\"{o}bius bundle. This provides a non-flat, non-spherical stable shrinker in higher codimension, in sharp contrast with the classification of stable hypersurface shrinkers. Topologically, the M\"obius sh...

Kahnrad Braxton, Tang-Kai Lee, Jonathan J. Zhu · 0 citations

Preprint Sep 2026

Uniqueness of free boundary minimal annuli

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 $(\Delta_{\mathbb{S}^2}+2)u=0$ on smooth spherical annuli with $u=0$ and $|\nabla u|=1$ on the boundary; their one-homogeneous extensions are the axia...

Davide Parise, Jonathan J. Zhu · 1 citation