https://neckpinch.com/authors/tobias-weth/New arXiv papers by Tobias Weth, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2301.12015/arxiv:2301.12015Fri, 27 Jan 2023 00:00:00 GMTFranziska Borer, Peter Elbau, Tobias Weth — On a closed Riemannian surface (M,bar g) with negative Euler characteristic, we study the problem of finding conformal metrics with prescribed volume A>0 and the property that their Gauss curvatures f_λ= f + λ are given as the sum of a prescribed function f ∈ C^∞(M) and an additive constant λ. Our main tool in this study is a new variant of the prescribed Gauss curvature flow, for which we establish local well-posedness and global compactness results. In contrast to previous work, our approach does not require any sign conditions on f. Moreover, we exhibit conditions under which the function f_λ is sign changing and the standard prescribed Gauss curvature flow is not applicable.Other curvature flowsGauss curvature flowSurfacesLimit spaces & RCD https://neckpinch.com/papers/2205.01248/arxiv:2205.01248Mon, 02 May 2022 00:00:00 GMTAnoumou Attiogbe, Mouahmed Moustapha Fall, Tobias Weth — We consider the geometric evolution problem of entire graphs moving by fractional mean curvature. For this, we study the associated nonlocal quasilinear evolution equation satisfied by the family of graph functions. We establish, using an analytic semigroup approach, short time existence, uniqueness and optimal Hölder regularity in time and space of classical solutions of the nonlocal equation, depending on the regularity of the initial graph. The method also yields C^∞-smoothness estimates of the evolving graphs for positive times.Mean curvature flowAnisotropic & nonlocal flowsStability & uniquenessHarmonic maps & DeTurck trick