Abstract: We prove that if a rescaled mean curvature flow is a global graph over the round cylinder with small gradient and converges at a super-exponential rate, then it must coincide with the cylinder itself. We also show that this result is sharp by constructing local graphical counterexamples with arbitrarily fast super-exponential convergence and rapidly expanding domains. These examples form infinite-dimensional families of Tikhonov-type solutions and show that unique continuation fails for local graphical solutions. Our constructions apply to a broad class of nonlinear equations. This talk is based on joint work with Yiqi Huang.

Brief biography: Xinrui Zhao is a Gibbs Assistant Professor in the Department of Mathematics at Yale University. He received his Ph.D. from MIT, where he was supervised by Prof. Tobias Colding. His research interests lie in geometric analysis, including mean curvature flow and RCD spaces.

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