Improved pseudolocality on large hyperbolic balls
We obtain an improved pseudolocality result for Ricci flows on two-dimensional surfaces that are initially almost-hyperbolic on large hyperbolic balls. We prove that, at the central point of the hyperbolic ball, the Gauss curvature remains close to the hyperbolic value for a time that grows exponent...
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| Format: | Journal article |
| Language: | English |
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International Press
2023
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| _version_ | 1797111487514279936 |
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| author | McLeod, AD |
| author_facet | McLeod, AD |
| author_sort | McLeod, AD |
| collection | OXFORD |
| description | We obtain an improved pseudolocality result for Ricci flows on two-dimensional surfaces that are initially almost-hyperbolic on large hyperbolic balls. We prove that, at the central point of the hyperbolic ball, the Gauss curvature remains close to the hyperbolic value for a time that grows exponentially in the radius of the ball. This two-dimensional result allows us to precisely conjecture how the phenomenon should appear in the higher dimensional setting. |
| first_indexed | 2024-03-07T08:09:36Z |
| format | Journal article |
| id | oxford-uuid:6dab8266-7504-4ffa-903e-1f8894f6b5db |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T08:09:36Z |
| publishDate | 2023 |
| publisher | International Press |
| record_format | dspace |
| spelling | oxford-uuid:6dab8266-7504-4ffa-903e-1f8894f6b5db2023-11-20T09:39:43ZImproved pseudolocality on large hyperbolic ballsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:6dab8266-7504-4ffa-903e-1f8894f6b5dbEnglishSymplectic ElementsInternational Press2023McLeod, ADWe obtain an improved pseudolocality result for Ricci flows on two-dimensional surfaces that are initially almost-hyperbolic on large hyperbolic balls. We prove that, at the central point of the hyperbolic ball, the Gauss curvature remains close to the hyperbolic value for a time that grows exponentially in the radius of the ball. This two-dimensional result allows us to precisely conjecture how the phenomenon should appear in the higher dimensional setting. |
| spellingShingle | McLeod, AD Improved pseudolocality on large hyperbolic balls |
| title | Improved pseudolocality on large hyperbolic balls |
| title_full | Improved pseudolocality on large hyperbolic balls |
| title_fullStr | Improved pseudolocality on large hyperbolic balls |
| title_full_unstemmed | Improved pseudolocality on large hyperbolic balls |
| title_short | Improved pseudolocality on large hyperbolic balls |
| title_sort | improved pseudolocality on large hyperbolic balls |
| work_keys_str_mv | AT mcleodad improvedpseudolocalityonlargehyperbolicballs |