Łojasiewicz inequalities near simple bubble trees
In this paper we prove a gap phenomenon for critical points of the $H$-functional on closed non-spherical surfaces when $H$ is constant, and in this setting furthermore prove that sequences of almost critical points satisfy Łojasiewicz inequalities as they approach the first non-trivial bubble tree...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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Johns Hopkins University Press
2024
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| _version_ | 1826317078505717760 |
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| author | Malchiodi, A Rupflin, M Sharp, B |
| author_facet | Malchiodi, A Rupflin, M Sharp, B |
| author_sort | Malchiodi, A |
| collection | OXFORD |
| description | In this paper we prove a gap phenomenon for critical points of the $H$-functional on closed non-spherical surfaces when $H$ is constant, and in this setting furthermore prove that sequences of almost critical points satisfy Łojasiewicz inequalities as they approach the first non-trivial bubble tree.
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To prove these results we derive sufficient conditions for Łojasiewicz inequalities to hold near a finite-dimensional submanifold of almost-critical points for suitable functionals on a Hilbert space. |
| first_indexed | 2024-03-07T08:12:22Z |
| format | Journal article |
| id | oxford-uuid:382a2b4e-b24e-4e55-86dc-1e5ef158fee6 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2025-02-19T04:32:51Z |
| publishDate | 2024 |
| publisher | Johns Hopkins University Press |
| record_format | dspace |
| spelling | oxford-uuid:382a2b4e-b24e-4e55-86dc-1e5ef158fee62025-01-20T14:13:34ZŁojasiewicz inequalities near simple bubble treesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:382a2b4e-b24e-4e55-86dc-1e5ef158fee6EnglishSymplectic ElementsJohns Hopkins University Press2024Malchiodi, ARupflin, MSharp, BIn this paper we prove a gap phenomenon for critical points of the $H$-functional on closed non-spherical surfaces when $H$ is constant, and in this setting furthermore prove that sequences of almost critical points satisfy Łojasiewicz inequalities as they approach the first non-trivial bubble tree. <br> To prove these results we derive sufficient conditions for Łojasiewicz inequalities to hold near a finite-dimensional submanifold of almost-critical points for suitable functionals on a Hilbert space. |
| spellingShingle | Malchiodi, A Rupflin, M Sharp, B Łojasiewicz inequalities near simple bubble trees |
| title | Łojasiewicz inequalities near simple bubble trees |
| title_full | Łojasiewicz inequalities near simple bubble trees |
| title_fullStr | Łojasiewicz inequalities near simple bubble trees |
| title_full_unstemmed | Łojasiewicz inequalities near simple bubble trees |
| title_short | Łojasiewicz inequalities near simple bubble trees |
| title_sort | lojasiewicz inequalities near simple bubble trees |
| work_keys_str_mv | AT malchiodia łojasiewiczinequalitiesnearsimplebubbletrees AT rupflinm łojasiewiczinequalitiesnearsimplebubbletrees AT sharpb łojasiewiczinequalitiesnearsimplebubbletrees |