淡江大學機構典藏:Item 987654321/124457
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    Please use this identifier to cite or link to this item: https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/124457


    Title: Sobolev inequality and isoperimetric inequality for submanifolds in a smooth metric measure space
    Authors: Ho, Pak-tung
    Keywords: Smooth metric measure space;Sobolev inequality;logarithmic Sobolev inequality
    Date: 2023-03-29
    Issue Date: 2023-09-07 12:05:34 (UTC+8)
    Publisher: World Scientific
    Abstract: Brendle recently proved a sharp Sobolev inequality and logarithmic Sobolev inequality for submanifolds in Euclidean space. From the sharp Sobolev inequality, he achieved a breakthrough in the conjecture of isoperimetric inequality for minimal submanifolds. In this paper, we extend Brendle’s results to submanifolds in a smooth metric measure space. As an application, we prove some new isoperimetric-type inequalities in some smooth metric measure spaces. For example, we obtain a new isoperimetric-type inequality for self-expander.
    Relation: International Journal of Mathematics 34(5),　2350027
    DOI: 10.1142/S0129167X23500271
    Appears in Collections:[Department of Applied Mathematics and Data Science] Journal Article

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