The $\gamma $-support as a micro-support
We prove that for any element $L$ in the completion of the space of smooth compact exact Lagrangian submanifolds of a cotangent bundle equipped with the spectral distance, the $\gamma $-support of $L$ coincides with the reduced micro-support of its sheaf quantization. As an application, we give a ch...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2023-10-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.499/ |
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| _version_ | 1825206206907547648 |
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| author | Asano, Tomohiro Guillermou, Stéphane Humilière, Vincent Ike, Yuichi Viterbo, Claude |
| author_facet | Asano, Tomohiro Guillermou, Stéphane Humilière, Vincent Ike, Yuichi Viterbo, Claude |
| author_sort | Asano, Tomohiro |
| collection | DOAJ |
| description | We prove that for any element $L$ in the completion of the space of smooth compact exact Lagrangian submanifolds of a cotangent bundle equipped with the spectral distance, the $\gamma $-support of $L$ coincides with the reduced micro-support of its sheaf quantization. As an application, we give a characterization of the Vichery subdifferential in terms of $\gamma $-support. |
| format | Article |
| id | doaj-art-0b2ead7c739f43e0aec9b182048d1ca3 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2023-10-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-0b2ead7c739f43e0aec9b182048d1ca32025-02-07T11:10:23ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-10-01361G81333134010.5802/crmath.49910.5802/crmath.499The $\gamma $-support as a micro-supportAsano, Tomohiro0Guillermou, Stéphane1Humilière, Vincent2Ike, Yuichi3Viterbo, Claude4Faculty of Electrical, Information and Communication Engineering, Institute of Science and Engineering, Kanazawa University, Kakumamachi, Kanazawa, 920-1192, JapanUMR CNRS 6629 du CNRS Laboratoire de Mathématiques Jean LERAY 2 Chemin de la Houssinière, BP 92208, F-44322 NANTES Cedex 3 FranceSorbonne Université and Université de Paris, CNRS, IMJ-PRG, F-75005 Paris, France and Institut Universitaire de FranceGraduate School of Information Science and Technology, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, JapanUniversité Paris-Saclay, CNRS, Laboratoire de mathématiques d’Orsay, 91405, Orsay, FranceWe prove that for any element $L$ in the completion of the space of smooth compact exact Lagrangian submanifolds of a cotangent bundle equipped with the spectral distance, the $\gamma $-support of $L$ coincides with the reduced micro-support of its sheaf quantization. As an application, we give a characterization of the Vichery subdifferential in terms of $\gamma $-support.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.499/ |
| spellingShingle | Asano, Tomohiro Guillermou, Stéphane Humilière, Vincent Ike, Yuichi Viterbo, Claude The $\gamma $-support as a micro-support Comptes Rendus. Mathématique |
| title | The $\gamma $-support as a micro-support |
| title_full | The $\gamma $-support as a micro-support |
| title_fullStr | The $\gamma $-support as a micro-support |
| title_full_unstemmed | The $\gamma $-support as a micro-support |
| title_short | The $\gamma $-support as a micro-support |
| title_sort | gamma support as a micro support |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.499/ |
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