https://neckpinch.com/authors/paula-burkhardt-guim/New arXiv papers by Paula Burkhardt-Guim, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2609.25550/arxiv:2609.25550Tue, 22 Sep 2026 00:00:00 GMTPaula Burkhardt-Guim — We prove a Positive Mass Theorem for C⁰-asymptotically flat Riemannian metrics with nonnegative scalar curvature in a weak sense that are sufficiently uniformly close to Euclidean space. More precisely, we show that a C⁰-asymptotically flat Riemannian metric that is a C⁰ perturbation of Euclidean space with nonnegative scalar curvature in the sense of Ricci flow has nonnegative mass, where the mass is given by a C⁰ analog of the classical ADM mass previously introduced by the author.Ricci flowScalar curvatureBoundaries & non-compactPhysics https://neckpinch.com/papers/2208.14550/arxiv:2208.14550Tue, 30 Aug 2022 00:00:00 GMTPaula Burkhardt-Guim — We show that there exists a quantity, depending only on C⁰ data of a Riemannian metric, that agrees with the usual ADM mass at infinity whenever the ADM mass exists, but has a well-defined limit at infinity for any continuous Riemannian metric that is asymptotically flat in the C⁰ sense and has nonnegative scalar curvature in the sense of Ricci flow. Moreover, the C⁰ mass at infinity is independent of choice of C⁰-asymptotically flat coordinate chart, and the C⁰ local mass has controlled distortion under Ricci-DeTurck flow when coupled with a suitably evolving test function.Ricci flowScalar curvatureBoundaries & non-compactHarmonic maps & DeTurck trickPhysics