On the Stability of Killing Cylinders in Hyperbolic Space
In this paper we study the stability of a Killing cylinder in hyperbolic 3-space when regarded as a capillary surface for the partitioning problem. In contrast with the Euclidean case, we consider a variety of totally umbilical support surfaces, including horospheres, totally geodesic planes, equidi...
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| Veröffentlicht in: | The Journal of geometric analysis 2024-09, Vol.34 (9), Article 281 |
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| creator | Bueno, Antonio López, Rafael |
| description | In this paper we study the stability of a Killing cylinder in hyperbolic 3-space when regarded as a capillary surface for the partitioning problem. In contrast with the Euclidean case, we consider a variety of totally umbilical support surfaces, including horospheres, totally geodesic planes, equidistant surfaces and round spheres. In all of them, we explicitly compute the Morse index of the corresponding eigenvalue problem for the Jacobi operator. We also address the stability of compact pieces of Killing cylinders with Dirichlet boundary conditions when the boundary is formed by two fixed circles, exhibiting an analogous to the Plateau–Rayleigh instability criterion for Killing cylinders in the Euclidean space. Finally, we prove that the Delaunay surfaces can be obtained by bifurcating Killing cylinders supported on geodesic planes. |
| doi_str_mv | 10.1007/s12220-024-01720-8 |
| format | Article |
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Finally, we prove that the Delaunay surfaces can be obtained by bifurcating Killing cylinders supported on geodesic planes.</description><subject>Abstract Harmonic Analysis</subject><subject>Boundary conditions</subject><subject>Convex and Discrete Geometry</subject><subject>Cylinders</subject><subject>Differential Geometry</subject><subject>Dynamical Systems and Ergodic Theory</subject><subject>Eigenvalues</subject><subject>Euclidean geometry</subject><subject>Fourier Analysis</subject><subject>Global Analysis and Analysis on Manifolds</subject><subject>Hyperbolic coordinates</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Stability criteria</subject><subject>Surface stability</subject><issn>1050-6926</issn><issn>1559-002X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNp9kEtLxDAUhYMoOD7-gKuA6-rNo0mzlEEdcWAWo-AupGkyZqhtTTqL_nujFdx57-KexTnnwofQFYEbAiBvE6GUQgGUF0BkVtURWpCyVAUAfTvOGkoohKLiFJ2ltAfggnG5QGrT4fHd4e1o6tCGccK9x8-hbUO3w8spn8bFhEOHV9PgYt23weLtYKy7QCfetMld_t5z9Ppw_7JcFevN49Pybl1YCjAW3uTlQjW0UVB7UMAk9aWQVhHrKqPyOM8kgaYSRjaCW86hbqynrqLKsHN0PfcOsf88uDTqfX-IXX6pGVQlAUa5zC46u2zsU4rO6yGGDxMnTUB_I9IzIp0R6R9EusohNodSNnc7F_-q_0l9AezxaA0</recordid><startdate>20240901</startdate><enddate>20240901</enddate><creator>Bueno, Antonio</creator><creator>López, Rafael</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0003-3108-7009</orcidid></search><sort><creationdate>20240901</creationdate><title>On the Stability of Killing Cylinders in Hyperbolic Space</title><author>Bueno, Antonio ; López, Rafael</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c200t-fafaf469d2d90bf090372f567c91ce8a9999ef3710d86a7d64c440bdcf2e829a3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Abstract Harmonic Analysis</topic><topic>Boundary conditions</topic><topic>Convex and Discrete Geometry</topic><topic>Cylinders</topic><topic>Differential Geometry</topic><topic>Dynamical Systems and Ergodic Theory</topic><topic>Eigenvalues</topic><topic>Euclidean geometry</topic><topic>Fourier Analysis</topic><topic>Global Analysis and Analysis on Manifolds</topic><topic>Hyperbolic coordinates</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Stability criteria</topic><topic>Surface stability</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Bueno, Antonio</creatorcontrib><creatorcontrib>López, Rafael</creatorcontrib><collection>CrossRef</collection><jtitle>The Journal of geometric analysis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Bueno, Antonio</au><au>López, Rafael</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On the Stability of Killing Cylinders in Hyperbolic Space</atitle><jtitle>The Journal of geometric analysis</jtitle><stitle>J Geom Anal</stitle><date>2024-09-01</date><risdate>2024</risdate><volume>34</volume><issue>9</issue><artnum>281</artnum><issn>1050-6926</issn><eissn>1559-002X</eissn><abstract>In this paper we study the stability of a Killing cylinder in hyperbolic 3-space when regarded as a capillary surface for the partitioning problem. 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| subjects | Abstract Harmonic Analysis Boundary conditions Convex and Discrete Geometry Cylinders Differential Geometry Dynamical Systems and Ergodic Theory Eigenvalues Euclidean geometry Fourier Analysis Global Analysis and Analysis on Manifolds Hyperbolic coordinates Mathematics Mathematics and Statistics Stability criteria Surface stability |
| title | On the Stability of Killing Cylinders in Hyperbolic Space |
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