https://neckpinch.com/authors/michael-struwe/New arXiv papers by Michael Struwe, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2401.13377arxiv:2401.13377Wed, 24 Jan 2024 00:00:00 GMTMichael Struwe — For given functions f and j on the disc B and its boundary ∂B=S¹, we study the existence of conformal metrics g=e^(2u)g₀ with prescribed Gauss curvature K_g=f and boundary geodesic curvature k_g=j. Using the variational characterization of such metrics obtained by Cruz-Blazquez and Ruiz (2018), we show that there is a canonical negative gradient flow of such metrics, either converging to a solution of the prescribed curvature problem, or blowing up to a spherical cap. In the latter case, similar to our work Struwe (2005) on the prescribed curvature problem on the sphere, we are able to exhibit a 2-dimensional shadow flow for the center of mass of the evolving metrics from which we obtain existence results complementing the results recently obtained by Ruiz (2021) by degree-theory.Other curvature flows