A Liouville type theorem for ancient Lagrangian mean curvature flows
We prove a Liouville type result for convex solutions of the Lagrangian mean curvature flow with restricted quadratic growth assumptions at antiquity on the solutions.
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| Published in | Communications in partial differential equations Vol. 50; no. 1-2; pp. 118 - 129 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Philadelphia
Taylor & Francis
01.02.2025
Taylor & Francis Ltd |
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| Online Access | Get full text |
| ISSN | 0360-5302 1532-4133 |
| DOI | 10.1080/03605302.2024.2439351 |
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| Abstract | We prove a Liouville type result for convex solutions of the Lagrangian mean curvature flow with restricted quadratic growth assumptions at antiquity on the solutions. |
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| AbstractList | We prove a Liouville type result for convex solutions of the Lagrangian mean curvature flow with restricted quadratic growth assumptions at antiquity on the solutions. |
| Author | Warren, Micah Bhattacharya, Arunima Weser, Daniel |
| Author_xml | – sequence: 1 givenname: Arunima surname: Bhattacharya fullname: Bhattacharya, Arunima organization: Department of Mathematics, Phillips Hall, the University of North Carolina at Chapel Hill – sequence: 2 givenname: Micah surname: Warren fullname: Warren, Micah organization: Department of Mathematics, University of Oregon – sequence: 3 givenname: Daniel surname: Weser fullname: Weser, Daniel organization: Department of Mathematics, Phillips Hall, the University of North Carolina at Chapel Hill |
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| Cites_doi | 10.1080/03605300801970986 10.4310/jdg/1090950193 10.1007/s00208-013-0897-2 10.1515/CRELLE.2011.102 10.1002/cpa.22130 10.1512/iumj.2003.52.2341 10.1007/s002220100201 10.4310/jdg/1729092459 10.1007/s00208-022-02430-8 10.1007/BF00281503 10.2140/pjm.2022.318.43 10.1007/BF02392726 10.1007/s00209-008-0403-9 10.1353/ajm.2003.0007 10.1002/cpa.20251 10.1073/pnas.69.4.821 10.1016/j.na.2019.05.006 10.1007/s10240-023-00143-5 10.1007/BF01232278 10.1002/cpa.20261 10.1007/BF02921385 10.1353/ajm.2014.0009 10.1353/ajm.0.0115 10.1007/s00526-024-02812-7 10.1007/s00526-021-02111-5 |
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| References | e_1_3_2_28_1 e_1_3_2_20_1 Tobias H. (e_1_3_2_10_1) 2004 e_1_3_2_21_1 e_1_3_2_22_1 e_1_3_2_23_1 e_1_3_2_24_1 e_1_3_2_25_1 e_1_3_2_26_1 Bhattacharya A. (e_1_3_2_34_1) 2023 Bhattacharya A. (e_1_3_2_29_1) 2024 Korevaar N. (e_1_3_2_5_1) 1986 e_1_3_2_16_1 e_1_3_2_9_1 e_1_3_2_17_1 e_1_3_2_8_1 e_1_3_2_18_1 e_1_3_2_7_1 e_1_3_2_19_1 e_1_3_2_2_1 e_1_3_2_31_1 Tu A. N. (e_1_3_2_6_1) 2011; 2011 e_1_3_2_30_1 e_1_3_2_33_1 e_1_3_2_11_1 e_1_3_2_32_1 e_1_3_2_12_1 e_1_3_2_35_1 e_1_3_2_13_1 Bhattacharya A. (e_1_3_2_27_1) 2021; 60 e_1_3_2_4_1 e_1_3_2_14_1 e_1_3_2_3_1 e_1_3_2_15_1 e_1_3_2_36_1 |
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| SubjectTerms | Curvature Lagrangian submanifolds Liouville result Liouville theorem mean curvature flow |
| Title | A Liouville type theorem for ancient Lagrangian mean curvature flows |
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