The stekloff problem for rotationally invariant metrics on the ball
Let (Br,g) be a ball of radius r and gt;0 in Rn (n≥ 2) endowed with a rotationally invariant metricds2+f2(s)dw2, where dw2 represents the standard metric on Sn-1, the (n-1)--dimensional unit sphere. Assume that Br has non--negative sectional curvature. In this paper we prove that ifh(r) and gt;0 is...
- Autores:
-
Montaño Carreño, Óscar Andrés
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2013
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/49342
- Acceso en línea:
- https://repositorio.unal.edu.co/handle/unal/49342
http://bdigital.unal.edu.co/42799/
- Palabra clave:
- Valor propio de Stekloff
métrica rotacionalmente invariante
curvatura seccional no negativa
35P15
53C20
53C42
53C43
Stekloff eigenvalue
Rotationally invariant metric
Non-negative sectional curvature
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
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Atribución-NoComercial 4.0 InternacionalDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Montaño Carreño, Óscar Andrés34851836-ef2d-48ab-854e-ebe340b6dfc63002019-06-29T08:36:38Z2019-06-29T08:36:38Z2013https://repositorio.unal.edu.co/handle/unal/49342http://bdigital.unal.edu.co/42799/Let (Br,g) be a ball of radius r and gt;0 in Rn (n≥ 2) endowed with a rotationally invariant metricds2+f2(s)dw2, where dw2 represents the standard metric on Sn-1, the (n-1)--dimensional unit sphere. Assume that Br has non--negative sectional curvature. In this paper we prove that ifh(r) and gt;0 is the mean curvature on ∂ Br and ν1 is the first eigenvalue of the Stekloff problem, thenν1 ≥ h(r). Equality (ν 1 = h(r)) holds only for the standard metric of Rn.Sea (Br,g) una bola de radio r and gt;0 en Rn (n≥ 2) dotada con una métrica g rotacionalmente invariante ds2+f2(s)dw2, donde dw2 representa la métrica estándar sobre Sn-1, la esfera unitaria (n-1)--dimensional. Asumamos que Br tiene curvatura seccional no negativa. En este artículo demostramos que si h(r) and gt;0 es la curvatura media sobre ∂ Br y ν1 es el primer valor propio del problema de Stekloff, entonces ν 1 ≥ h(r). La igualdad (ν 1 = h(r)) se tiene sólo si ges la métrica estándar de Rn.application/pdfspaUniversidad Nacuional de Colombia; Sociedad Colombiana de matemáticashttp://revistas.unal.edu.co/index.php/recolma/article/view/45185Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de MatemáticasRevista Colombiana de MatemáticasRevista Colombiana de Matemáticas; Vol. 47, núm. 2 (2013); 181-190 2357-4100 0034-7426Montaño Carreño, Óscar Andrés (2013) The stekloff problem for rotationally invariant metrics on the ball. Revista Colombiana de Matemáticas; Vol. 47, núm. 2 (2013); 181-190 2357-4100 0034-7426 .The stekloff problem for rotationally invariant metrics on the ballArtículo de revistainfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1http://purl.org/coar/version/c_970fb48d4fbd8a85Texthttp://purl.org/redcol/resource_type/ARTValor propio de Stekloffmétrica rotacionalmente invariantecurvatura seccional no negativa35P1553C2053C4253C43Stekloff eigenvalueRotationally invariant metricNon-negative sectional curvatureORIGINAL45185-216927-2-PB.htmltext/html5088https://repositorio.unal.edu.co/bitstream/unal/49342/1/45185-216927-2-PB.html713cd9364f56148f2191e27503cdb293MD5145185-216926-1-SM.pdfapplication/pdf438320https://repositorio.unal.edu.co/bitstream/unal/49342/2/45185-216926-1-SM.pdfb92c4a9255449c3988e85bef2c5a5365MD52THUMBNAIL45185-216926-1-SM.pdf.jpg45185-216926-1-SM.pdf.jpgGenerated Thumbnailimage/jpeg5448https://repositorio.unal.edu.co/bitstream/unal/49342/3/45185-216926-1-SM.pdf.jpgbaa612baa0abacd089ef6e1b5aabcc38MD53unal/49342oai:repositorio.unal.edu.co:unal/493422023-12-09 23:05:58.472Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co |
| dc.title.spa.fl_str_mv |
The stekloff problem for rotationally invariant metrics on the ball |
| title |
The stekloff problem for rotationally invariant metrics on the ball |
| spellingShingle |
The stekloff problem for rotationally invariant metrics on the ball Valor propio de Stekloff métrica rotacionalmente invariante curvatura seccional no negativa 35P15 53C20 53C42 53C43 Stekloff eigenvalue Rotationally invariant metric Non-negative sectional curvature |
| title_short |
The stekloff problem for rotationally invariant metrics on the ball |
| title_full |
The stekloff problem for rotationally invariant metrics on the ball |
| title_fullStr |
The stekloff problem for rotationally invariant metrics on the ball |
| title_full_unstemmed |
The stekloff problem for rotationally invariant metrics on the ball |
| title_sort |
The stekloff problem for rotationally invariant metrics on the ball |
| dc.creator.fl_str_mv |
Montaño Carreño, Óscar Andrés |
| dc.contributor.author.spa.fl_str_mv |
Montaño Carreño, Óscar Andrés |
| dc.subject.proposal.spa.fl_str_mv |
Valor propio de Stekloff métrica rotacionalmente invariante curvatura seccional no negativa 35P15 53C20 53C42 53C43 Stekloff eigenvalue Rotationally invariant metric Non-negative sectional curvature |
| topic |
Valor propio de Stekloff métrica rotacionalmente invariante curvatura seccional no negativa 35P15 53C20 53C42 53C43 Stekloff eigenvalue Rotationally invariant metric Non-negative sectional curvature |
| description |
Let (Br,g) be a ball of radius r and gt;0 in Rn (n≥ 2) endowed with a rotationally invariant metricds2+f2(s)dw2, where dw2 represents the standard metric on Sn-1, the (n-1)--dimensional unit sphere. Assume that Br has non--negative sectional curvature. In this paper we prove that ifh(r) and gt;0 is the mean curvature on ∂ Br and ν1 is the first eigenvalue of the Stekloff problem, thenν1 ≥ h(r). Equality (ν 1 = h(r)) holds only for the standard metric of Rn. |
| publishDate |
2013 |
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2013 |
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2019-06-29T08:36:38Z |
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2019-06-29T08:36:38Z |
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Artículo de revista |
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http://purl.org/coar/resource_type/c_2df8fbb1 |
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info:eu-repo/semantics/article |
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Text |
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https://repositorio.unal.edu.co/handle/unal/49342 |
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http://bdigital.unal.edu.co/42799/ |
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spa |
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spa |
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http://revistas.unal.edu.co/index.php/recolma/article/view/45185 |
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Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de Matemáticas Revista Colombiana de Matemáticas |
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Revista Colombiana de Matemáticas; Vol. 47, núm. 2 (2013); 181-190 2357-4100 0034-7426 |
| dc.relation.references.spa.fl_str_mv |
Montaño Carreño, Óscar Andrés (2013) The stekloff problem for rotationally invariant metrics on the ball. Revista Colombiana de Matemáticas; Vol. 47, núm. 2 (2013); 181-190 2357-4100 0034-7426 . |
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Derechos reservados - Universidad Nacional de Colombia |
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Atribución-NoComercial 4.0 Internacional |
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info:eu-repo/semantics/openAccess |
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