A Mountain‑Pass Theorem for Asymptotically Conical Self‑Expanders

作     者：Jacob Bernstein Lu Wang 

作者机构：Department of MathematicsJohns Hopkins University3400 N.Charles StreetBaltimoreMD 21218USA Department of MathematicsCalifornia Institute of Technology1200 E.California BoulevardPasadenaCA 91125USA Present Address:Department of MathematicsYale University10 Hillhouse AvenueNew HavenCT 06511USA 

出 版 物：《Peking Mathematical Journal》 (北京数学杂志（英文）)

年 卷 期：2022年第5卷第2期

页      面：213-278页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported by the NSF Grants DMS-1609340 and DMS-1904674,the Institute for Advanced Study with funding provided by the Charles Simonyi Endowment supported by the NSF Grants DMS-2018221(formerly DMS-1811144)and DMS-2018220(formerly DMS-1834824) the funding from the Wisconsin Alumni Research Foundation and a Vilas Early Career Investigator Award by the University of Wisconsin-Madison,and a von Neumann Fellowship by the Institute for Advanced Study with funding from the Zürich Insurance Company and the NSF Grant DMS-1638352 

主　　题：Self-expander Mean curvature flow Min-max theory 

摘      要：We develop a min–max theory for asymptotically conical self-expanders of mean curvature *** particular,we show that given two distinct strictly stable selfexpanders that are asymptotic to the same cone and bound a domain,there exists a new asymptotically conical self-expander trapped between the two.