The Obata equation with Robin boundary condition
We study the Obata equation with Robin boundary condition \partial f/\partial \nu + af = 0 on manifolds with boundary, where a is a non-zero constant. Dirichlet and Neumann boundary conditions were previously studied by Reilly, Escobar and Xia. Compared with their results, the sign of a plays an imp...
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| Veröffentlicht in: | Revista matemática iberoamericana 2021-03, Vol.37 (2), p.643-670 |
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| container_title | Revista matemática iberoamericana |
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| creator | Chen, Xuezhang Lai, Mijia Wang, Fang |
| description | We study the Obata equation with Robin boundary condition
\partial f/\partial \nu + af = 0
on manifolds with boundary, where
a
is a non-zero constant. Dirichlet and Neumann boundary conditions were previously studied by Reilly, Escobar and Xia. Compared with their results, the sign of
a
plays an important role here. The new discovery shows besides spherical domains, there are other manifolds for both
a > 0
and
a < 0
. We also consider the Obata equation with non-vanishing Neumann condition
\partial f/\partial \nu=1
. |
| doi_str_mv | 10.4171/RMI/1212 |
| format | Article |
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\partial f/\partial \nu + af = 0
on manifolds with boundary, where
a
is a non-zero constant. Dirichlet and Neumann boundary conditions were previously studied by Reilly, Escobar and Xia. Compared with their results, the sign of
a
plays an important role here. The new discovery shows besides spherical domains, there are other manifolds for both
a > 0
and
a < 0
. We also consider the Obata equation with non-vanishing Neumann condition
\partial f/\partial \nu=1
.</description><identifier>ISSN: 0213-2230</identifier><identifier>EISSN: 2235-0616</identifier><identifier>DOI: 10.4171/RMI/1212</identifier><language>eng</language><publisher>European Mathematical Society Publishing House</publisher><ispartof>Revista matemática iberoamericana, 2021-03, Vol.37 (2), p.643-670</ispartof><rights>COPYRIGHT 2021 European Mathematical Society Publishing House</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c328t-2db42be7ddf7885c333c5a4ac7a5365df5584876dfebc51b550dfbc1b7b9a8ad3</citedby></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,27901,27902</link.rule.ids></links><search><creatorcontrib>Chen, Xuezhang</creatorcontrib><creatorcontrib>Lai, Mijia</creatorcontrib><creatorcontrib>Wang, Fang</creatorcontrib><title>The Obata equation with Robin boundary condition</title><title>Revista matemática iberoamericana</title><description>We study the Obata equation with Robin boundary condition
\partial f/\partial \nu + af = 0
on manifolds with boundary, where
a
is a non-zero constant. Dirichlet and Neumann boundary conditions were previously studied by Reilly, Escobar and Xia. Compared with their results, the sign of
a
plays an important role here. The new discovery shows besides spherical domains, there are other manifolds for both
a > 0
and
a < 0
. We also consider the Obata equation with non-vanishing Neumann condition
\partial f/\partial \nu=1
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\partial f/\partial \nu + af = 0
on manifolds with boundary, where
a
is a non-zero constant. Dirichlet and Neumann boundary conditions were previously studied by Reilly, Escobar and Xia. Compared with their results, the sign of
a
plays an important role here. The new discovery shows besides spherical domains, there are other manifolds for both
a > 0
and
a < 0
. We also consider the Obata equation with non-vanishing Neumann condition
\partial f/\partial \nu=1
.</abstract><pub>European Mathematical Society Publishing House</pub><doi>10.4171/RMI/1212</doi><tpages>28</tpages><oa>free_for_read</oa></addata></record> |
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| source | European Mathematical Society Publishing House |
| title | The Obata equation with Robin boundary condition |
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