The Logarithmic Sobolev inequality on non-compact self-shrinkers
In the paper we establish an optimal logarithmic Sobolev inequality for complete, non-compact, properly embedded self-shrinkers in the Euclidean space, which generalizes a recent result of Brendle \cite{Brendle22} for closed self-shrinkers. We first provide a proof for the logarithmic Sobolev inequa...
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| creator | Wang, Guofang Xia, Chao Zhang, Xiqiang |
| description | In the paper we establish an optimal logarithmic Sobolev inequality for
complete, non-compact, properly embedded self-shrinkers in the Euclidean space,
which generalizes a recent result of Brendle \cite{Brendle22} for closed
self-shrinkers. We first provide a proof for the logarithmic Sobolev inequality
in the Euclidean space by using the Alexandrov-Bakelman-Pucci (ABP) method.
Then we use this approach to show an optimal logarithmic Sobolev inequality for
complete, non-compact, properly embedded self-shrinkers in the Euclidean space,
which is a sharp version of the result of Ecker in \cite{Ecker}. The proof is a
noncompact modification of Brendle's proof for closed submanifolds and has a
big potential to provide new inequalities in noncompact manifolds. |
| doi_str_mv | 10.48550/arxiv.2410.13601 |
| format | Article |
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complete, non-compact, properly embedded self-shrinkers in the Euclidean space,
which generalizes a recent result of Brendle \cite{Brendle22} for closed
self-shrinkers. We first provide a proof for the logarithmic Sobolev inequality
in the Euclidean space by using the Alexandrov-Bakelman-Pucci (ABP) method.
Then we use this approach to show an optimal logarithmic Sobolev inequality for
complete, non-compact, properly embedded self-shrinkers in the Euclidean space,
which is a sharp version of the result of Ecker in \cite{Ecker}. The proof is a
noncompact modification of Brendle's proof for closed submanifolds and has a
big potential to provide new inequalities in noncompact manifolds.</description><identifier>DOI: 10.48550/arxiv.2410.13601</identifier><language>eng</language><subject>Mathematics - Analysis of PDEs ; Mathematics - Differential Geometry</subject><creationdate>2024-10</creationdate><rights>http://creativecommons.org/licenses/by-sa/4.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2410.13601$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2410.13601$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Wang, Guofang</creatorcontrib><creatorcontrib>Xia, Chao</creatorcontrib><creatorcontrib>Zhang, Xiqiang</creatorcontrib><title>The Logarithmic Sobolev inequality on non-compact self-shrinkers</title><description>In the paper we establish an optimal logarithmic Sobolev inequality for
complete, non-compact, properly embedded self-shrinkers in the Euclidean space,
which generalizes a recent result of Brendle \cite{Brendle22} for closed
self-shrinkers. We first provide a proof for the logarithmic Sobolev inequality
in the Euclidean space by using the Alexandrov-Bakelman-Pucci (ABP) method.
Then we use this approach to show an optimal logarithmic Sobolev inequality for
complete, non-compact, properly embedded self-shrinkers in the Euclidean space,
which is a sharp version of the result of Ecker in \cite{Ecker}. The proof is a
noncompact modification of Brendle's proof for closed submanifolds and has a
big potential to provide new inequalities in noncompact manifolds.</description><subject>Mathematics - Analysis of PDEs</subject><subject>Mathematics - Differential Geometry</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNpjYJA0NNAzsTA1NdBPLKrILNMzMgEKGBqbGRhyMjiEZKQq-OSnJxZllmTkZiYrBOcn5eeklilk5qUWlibmZJZUKuTnKeTl5-km5-cWJCaXKBSn5qTpFmcUZeZlpxYV8zCwpiXmFKfyQmluBnk31xBnD12wXfEFRZm5iUWV8SA748F2GhNWAQAYwDcJ</recordid><startdate>20241017</startdate><enddate>20241017</enddate><creator>Wang, Guofang</creator><creator>Xia, Chao</creator><creator>Zhang, Xiqiang</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20241017</creationdate><title>The Logarithmic Sobolev inequality on non-compact self-shrinkers</title><author>Wang, Guofang ; Xia, Chao ; Zhang, Xiqiang</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-arxiv_primary_2410_136013</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Mathematics - Analysis of PDEs</topic><topic>Mathematics - Differential Geometry</topic><toplevel>online_resources</toplevel><creatorcontrib>Wang, Guofang</creatorcontrib><creatorcontrib>Xia, Chao</creatorcontrib><creatorcontrib>Zhang, Xiqiang</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Wang, Guofang</au><au>Xia, Chao</au><au>Zhang, Xiqiang</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The Logarithmic Sobolev inequality on non-compact self-shrinkers</atitle><date>2024-10-17</date><risdate>2024</risdate><abstract>In the paper we establish an optimal logarithmic Sobolev inequality for
complete, non-compact, properly embedded self-shrinkers in the Euclidean space,
which generalizes a recent result of Brendle \cite{Brendle22} for closed
self-shrinkers. We first provide a proof for the logarithmic Sobolev inequality
in the Euclidean space by using the Alexandrov-Bakelman-Pucci (ABP) method.
Then we use this approach to show an optimal logarithmic Sobolev inequality for
complete, non-compact, properly embedded self-shrinkers in the Euclidean space,
which is a sharp version of the result of Ecker in \cite{Ecker}. The proof is a
noncompact modification of Brendle's proof for closed submanifolds and has a
big potential to provide new inequalities in noncompact manifolds.</abstract><doi>10.48550/arxiv.2410.13601</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Analysis of PDEs Mathematics - Differential Geometry |
| title | The Logarithmic Sobolev inequality on non-compact self-shrinkers |
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