PreprintarXiv licencearXiv
A continuous Positive Mass Theorem for perturbations of Euclidean space
Abstract
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.
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BibTeX
@misc{burkhardtguim2026continuous,
title = {{A continuous Positive Mass Theorem for perturbations of Euclidean space}},
author = {Paula Burkhardt-Guim},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25550},
eprint = {2609.25550},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25550},
}
RIS
TY - UNPB
TI - A continuous Positive Mass Theorem for perturbations of Euclidean space
AU - Paula Burkhardt-Guim
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.25550
UR - https://arxiv.org/abs/2609.25550
AB - We prove a Positive Mass Theorem for C^0-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 C^0-asymptotically flat Riemannian metric that is a C^0 perturbation of Euclidean space with nonnegative scalar curvature in the sense of Ricci flow has nonnegative mass, where the mass is given by a C^0 analog of the classical ADM mass previously introduced by the author.
ER -