https://neckpinch.com/authors/franziska-borer/New arXiv papers by Franziska Borer, 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