Horospheres and Convex Bodies in n-Dimensional Hyperbolic Space
Abstract In n-dimensional Euclidean space, the measure of hyperplanes intersecting a convex domain is proportional to the (n−2)-mean curvature integral of its boundary. This question was considered by Santaló in hyperbolic space. In non-Euclidean geometry the totally geodesic hypersurfaces are not a...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Gallego, E. [verfasserIn] |
|---|
| Format: |
Artikel |
|---|---|
| Sprache: |
Englisch |
| Erschienen: |
2004 |
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| Anmerkung: |
© Kluwer Academic Publishers 2004 |
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| Übergeordnetes Werk: |
Enthalten in: Geometriae dedicata - Kluwer Academic Publishers, 1972, 103(2004), 1 vom: Feb., Seite 103-114 |
|---|---|
| Übergeordnetes Werk: |
volume:103 ; year:2004 ; number:1 ; month:02 ; pages:103-114 |
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10.1023/B:GEOM.0000013945.66390.ca |
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| 520 | |a Abstract In n-dimensional Euclidean space, the measure of hyperplanes intersecting a convex domain is proportional to the (n−2)-mean curvature integral of its boundary. This question was considered by Santaló in hyperbolic space. In non-Euclidean geometry the totally geodesic hypersurfaces are not always the best analogue to linear hyperplanes. In some situations horospheres play the role of Euclidean hyperplanes. In dimensions n=2 and 3, Santaló proved that the measure of horospheres intersecting a convex domain is also proportional to the (n−2)-mean curvature integral of its boundary. In this paper we show that this analogy does not generalize to higher dimensions. We express the measure of horospheres intersecting a convex body as a linear combination of the mean curvature integrals of its boundary. | ||
| 700 | 1 | |a Naveira, A. M. |4 aut | |
| 700 | 1 | |a Solanes, G. |4 aut | |
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10.1023/B:GEOM.0000013945.66390.ca doi (DE-627)OLC2039052755 (DE-He213)B:GEOM.0000013945.66390.ca-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Gallego, E. verfasserin aut Horospheres and Convex Bodies in n-Dimensional Hyperbolic Space 2004 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Kluwer Academic Publishers 2004 Abstract In n-dimensional Euclidean space, the measure of hyperplanes intersecting a convex domain is proportional to the (n−2)-mean curvature integral of its boundary. This question was considered by Santaló in hyperbolic space. In non-Euclidean geometry the totally geodesic hypersurfaces are not always the best analogue to linear hyperplanes. In some situations horospheres play the role of Euclidean hyperplanes. In dimensions n=2 and 3, Santaló proved that the measure of horospheres intersecting a convex domain is also proportional to the (n−2)-mean curvature integral of its boundary. In this paper we show that this analogy does not generalize to higher dimensions. We express the measure of horospheres intersecting a convex body as a linear combination of the mean curvature integrals of its boundary. Naveira, A. M. aut Solanes, G. aut Enthalten in Geometriae dedicata Kluwer Academic Publishers, 1972 103(2004), 1 vom: Feb., Seite 103-114 (DE-627)129385301 (DE-600)183909-3 (DE-576)014772213 0046-5755 nnns volume:103 year:2004 number:1 month:02 pages:103-114 https://doi.org/10.1023/B:GEOM.0000013945.66390.ca lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_40 GBV_ILN_70 GBV_ILN_285 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2012 GBV_ILN_2015 GBV_ILN_2088 GBV_ILN_4116 GBV_ILN_4126 GBV_ILN_4316 AR 103 2004 1 02 103-114 |
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10.1023/B:GEOM.0000013945.66390.ca doi (DE-627)OLC2039052755 (DE-He213)B:GEOM.0000013945.66390.ca-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Gallego, E. verfasserin aut Horospheres and Convex Bodies in n-Dimensional Hyperbolic Space 2004 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Kluwer Academic Publishers 2004 Abstract In n-dimensional Euclidean space, the measure of hyperplanes intersecting a convex domain is proportional to the (n−2)-mean curvature integral of its boundary. This question was considered by Santaló in hyperbolic space. In non-Euclidean geometry the totally geodesic hypersurfaces are not always the best analogue to linear hyperplanes. In some situations horospheres play the role of Euclidean hyperplanes. In dimensions n=2 and 3, Santaló proved that the measure of horospheres intersecting a convex domain is also proportional to the (n−2)-mean curvature integral of its boundary. In this paper we show that this analogy does not generalize to higher dimensions. We express the measure of horospheres intersecting a convex body as a linear combination of the mean curvature integrals of its boundary. Naveira, A. M. aut Solanes, G. aut Enthalten in Geometriae dedicata Kluwer Academic Publishers, 1972 103(2004), 1 vom: Feb., Seite 103-114 (DE-627)129385301 (DE-600)183909-3 (DE-576)014772213 0046-5755 nnns volume:103 year:2004 number:1 month:02 pages:103-114 https://doi.org/10.1023/B:GEOM.0000013945.66390.ca lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_40 GBV_ILN_70 GBV_ILN_285 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2012 GBV_ILN_2015 GBV_ILN_2088 GBV_ILN_4116 GBV_ILN_4126 GBV_ILN_4316 AR 103 2004 1 02 103-114 |
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Horospheres and Convex Bodies in n-Dimensional Hyperbolic Space |
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Abstract In n-dimensional Euclidean space, the measure of hyperplanes intersecting a convex domain is proportional to the (n−2)-mean curvature integral of its boundary. This question was considered by Santaló in hyperbolic space. In non-Euclidean geometry the totally geodesic hypersurfaces are not always the best analogue to linear hyperplanes. In some situations horospheres play the role of Euclidean hyperplanes. In dimensions n=2 and 3, Santaló proved that the measure of horospheres intersecting a convex domain is also proportional to the (n−2)-mean curvature integral of its boundary. In this paper we show that this analogy does not generalize to higher dimensions. We express the measure of horospheres intersecting a convex body as a linear combination of the mean curvature integrals of its boundary. © Kluwer Academic Publishers 2004 |
| abstractGer |
Abstract In n-dimensional Euclidean space, the measure of hyperplanes intersecting a convex domain is proportional to the (n−2)-mean curvature integral of its boundary. This question was considered by Santaló in hyperbolic space. In non-Euclidean geometry the totally geodesic hypersurfaces are not always the best analogue to linear hyperplanes. In some situations horospheres play the role of Euclidean hyperplanes. In dimensions n=2 and 3, Santaló proved that the measure of horospheres intersecting a convex domain is also proportional to the (n−2)-mean curvature integral of its boundary. In this paper we show that this analogy does not generalize to higher dimensions. We express the measure of horospheres intersecting a convex body as a linear combination of the mean curvature integrals of its boundary. © Kluwer Academic Publishers 2004 |
| abstract_unstemmed |
Abstract In n-dimensional Euclidean space, the measure of hyperplanes intersecting a convex domain is proportional to the (n−2)-mean curvature integral of its boundary. This question was considered by Santaló in hyperbolic space. In non-Euclidean geometry the totally geodesic hypersurfaces are not always the best analogue to linear hyperplanes. In some situations horospheres play the role of Euclidean hyperplanes. In dimensions n=2 and 3, Santaló proved that the measure of horospheres intersecting a convex domain is also proportional to the (n−2)-mean curvature integral of its boundary. In this paper we show that this analogy does not generalize to higher dimensions. We express the measure of horospheres intersecting a convex body as a linear combination of the mean curvature integrals of its boundary. © Kluwer Academic Publishers 2004 |
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| title_short |
Horospheres and Convex Bodies in n-Dimensional Hyperbolic Space |
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https://doi.org/10.1023/B:GEOM.0000013945.66390.ca |
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Naveira, A. M. Solanes, G. |
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Naveira, A. M. Solanes, G. |
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| up_date |
2024-07-03T21:22:57.696Z |
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