Defining Pointwise Lower Scalar Curvature Bounds for 𝐶⁰ Metrics with Regularization by Ricci Flow

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dc.contributor.authorBurkhardt-Guim, Paula
dc.date.accessioned2025-12-23T13:13:38Z
dc.date.issued2020
dc.description.abstractWe survey some recent work using Ricci flow to create a class of local definitions of weak lower scalar curvature bounds that is well defined for 𝐶⁰ metrics. We discuss several properties of these definitions and explain some applications of this approach to questions regarding uniform convergence of metrics with scalar curvature bounded below. Finally, we consider the relationship between this approach and some other generalized notions of lower scalar curvature bounds.
dc.description.sponsorshipThis survey is dedicated to Misha Gromov on the occasion of his 75th birthday. I would like to thank him for his interest in my work. I would also like to thank my advisor, Richard Bamler, for his guidance during the writing process. Finally, I would like to thank the referees for numerous helpful comments on a previous draft of this paper. This material is based upon work supported by the National Science Foundation Graduate Research Fellowship Program under Grant No. DGE 1752814.
dc.identifier.citationDefining Pointwise Lower Scalar Curvature Bounds for 𝐶⁰ Metrics with Regularization by Ricci Flow. Paula Burkhardt-Guim. SIGMA 16 (2020), 128, 10 pages
dc.identifier.doihttps://doi.org/10.3842/SIGMA.2020.128
dc.identifier.issn1815-0659
dc.identifier.other2020 Mathematics Subject Classification: 53E20; 53C21
dc.identifier.otherarXiv:2007.14967
dc.identifier.urihttps://nasplib.isofts.kiev.ua/handle/123456789/211091
dc.language.isoen
dc.publisherІнститут математики НАН України
dc.relation.ispartofSymmetry, Integrability and Geometry: Methods and Applications
dc.statuspublished earlier
dc.titleDefining Pointwise Lower Scalar Curvature Bounds for 𝐶⁰ Metrics with Regularization by Ricci Flow
dc.typeArticle

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Symmetry, Integrability and Geometry: Methods and Applications, 2020, том 16, випуск за цей рік