Defining Pointwise Lower Scalar Curvature Bounds for ⁰ Metrics with Regularization by Ricci Flow
We 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 ⁰ metrics. We discuss several properties of these definitions and explain some applications of this approach to questions regarding uniform convergence of...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2020 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2020
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/211091 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Defining Pointwise Lower Scalar Curvature Bounds for ⁰ Metrics with Regularization by Ricci Flow. Paula Burkhardt-Guim. SIGMA 16 (2020), 128, 10 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | We 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 ⁰ 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.
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| ISSN: | 1815-0659 |