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...
Saved in:
| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2020 |
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2020
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/211091 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| 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 |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862559548060991488 |
|---|---|
| author | Burkhardt-Guim, Paula |
| author_facet | Burkhardt-Guim, Paula |
| citation_txt | Defining Pointwise Lower Scalar Curvature Bounds for ⁰ Metrics with Regularization by Ricci Flow. Paula Burkhardt-Guim. SIGMA 16 (2020), 128, 10 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
|
| first_indexed | 2026-03-13T07:46:09Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211091 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-13T07:46:09Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Burkhardt-Guim, Paula 2025-12-23T13:13:38Z 2020 Defining Pointwise Lower Scalar Curvature Bounds for ⁰ Metrics with Regularization by Ricci Flow. Paula Burkhardt-Guim. SIGMA 16 (2020), 128, 10 pages 1815-0659 2020 Mathematics Subject Classification: 53E20; 53C21 arXiv:2007.14967 https://nasplib.isofts.kiev.ua/handle/123456789/211091 https://doi.org/10.3842/SIGMA.2020.128 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. This 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Defining Pointwise Lower Scalar Curvature Bounds for ⁰ Metrics with Regularization by Ricci Flow Article published earlier |
| spellingShingle | Defining Pointwise Lower Scalar Curvature Bounds for ⁰ Metrics with Regularization by Ricci Flow Burkhardt-Guim, Paula |
| title | Defining Pointwise Lower Scalar Curvature Bounds for ⁰ Metrics with Regularization by Ricci Flow |
| title_full | Defining Pointwise Lower Scalar Curvature Bounds for ⁰ Metrics with Regularization by Ricci Flow |
| title_fullStr | Defining Pointwise Lower Scalar Curvature Bounds for ⁰ Metrics with Regularization by Ricci Flow |
| title_full_unstemmed | Defining Pointwise Lower Scalar Curvature Bounds for ⁰ Metrics with Regularization by Ricci Flow |
| title_short | Defining Pointwise Lower Scalar Curvature Bounds for ⁰ Metrics with Regularization by Ricci Flow |
| title_sort | defining pointwise lower scalar curvature bounds for ⁰ metrics with regularization by ricci flow |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211091 |
| work_keys_str_mv | AT burkhardtguimpaula definingpointwiselowerscalarcurvatureboundsfor0metricswithregularizationbyricciflow |