Abstract:
For some centrally symmetric convex bodies K CRn, we study the energy integral where the supremum runs over all finite signed Borel measures μ on K of total mass one. In the case where K = Bn q, the unit ball of Bnq (for 1<q ≤ 2) or an ellipsoid, we obtain the exact value or the correct asymptotical behavior of the supremum of these integrals. We apply these results to a classical embedding problem in metric geometry. We consider in Rn the Euclidean distance d2. For 0<α<1, we estimate the minimum R for which the snowflaked metric space (K,dα2) may be isometrically embedded on the surface of a Hilbert sphere of radius R. © 2014 The Author(s).
Registro:
Documento: |
Artículo
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Título: | Energy integrals and metric embedding theory |
Autor: | Carando, D.; Galicer, D.; Pinasco, D. |
Filiación: | Departamento de Matematica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pab. i, Cdad Universitaria (C1428EGA), Buenos Aires, Argentina IMAS-CONICET, Argentina Departamento de Matematicas y Estadstica, Universidad T. di Tella, Av. Figueroa Alcorta 7350, Buenos Aires, C1428BCW, Argentina CONICET, Argentina
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Año: | 2015
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Volumen: | 2015
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Número: | 16
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Página de inicio: | 7417
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Página de fin: | 7435
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DOI: |
http://dx.doi.org/10.1093/imrn/rnu169 |
Título revista: | International Mathematics Research Notices
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Título revista abreviado: | Int. Math. Res. Not.
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ISSN: | 10737928
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10737928_v2015_n16_p7417_Carando |
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Citas:
---------- APA ----------
Carando, D., Galicer, D. & Pinasco, D.
(2015)
. Energy integrals and metric embedding theory. International Mathematics Research Notices, 2015(16), 7417-7435.
http://dx.doi.org/10.1093/imrn/rnu169---------- CHICAGO ----------
Carando, D., Galicer, D., Pinasco, D.
"Energy integrals and metric embedding theory"
. International Mathematics Research Notices 2015, no. 16
(2015) : 7417-7435.
http://dx.doi.org/10.1093/imrn/rnu169---------- MLA ----------
Carando, D., Galicer, D., Pinasco, D.
"Energy integrals and metric embedding theory"
. International Mathematics Research Notices, vol. 2015, no. 16, 2015, pp. 7417-7435.
http://dx.doi.org/10.1093/imrn/rnu169---------- VANCOUVER ----------
Carando, D., Galicer, D., Pinasco, D. Energy integrals and metric embedding theory. Int. Math. Res. Not. 2015;2015(16):7417-7435.
http://dx.doi.org/10.1093/imrn/rnu169