The logarithmic Minkowski problem
Authors:
Károly J. Böröczky, Erwin Lutwak, Deane Yang and Gaoyong Zhang
Journal:
J. Amer. Math. Soc. 26 (2013), 831-852
MSC (2010):
Primary 52A40
DOI:
https://doi.org/10.1090/S0894-0347-2012-00741-3
Published electronically:
June 5, 2012
MathSciNet review:
3037788
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: In analogy with the classical Minkowski problem, necessary and sufficient conditions are given to assure that a given measure on the unit sphere is the cone-volume measure of the unit ball of a finite-dimensional Banach space.
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Additional Information
Károly J. Böröczky
Affiliation:
Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences
Email:
carlos@renyi.hu
Erwin Lutwak
Affiliation:
Department of Mathematics, Polytechnic Institute of New York University, Brooklyn, New York 11201
Email:
elutwak@poly.edu
Deane Yang
Affiliation:
Department of Mathematics, Polytechnic Institute of New York University, Brooklyn, New York 11201
ORCID:
0000-0002-4655-1428
Email:
dyang@poly.edu
Gaoyong Zhang
Affiliation:
Department of Mathematics, Polytechnic Institute of New York University, Brooklyn, New York 11201
Email:
gzhang@poly.edu
Keywords:
Cone-volume measure,
Minkowski problem,
$L_p$-Minkowski problem,
log-Minkowski problem
Received by editor(s):
September 18, 2011
Received by editor(s) in revised form:
February 7, 2012
Published electronically:
June 5, 2012
Additional Notes:
The research of the first author was supported, in part, by EU FP7 IEF grant GEOSUMSET and OTKA 075016.
The research of the other three authors was supported, in part, by NSF Grant DMS-1007347.
Article copyright:
© Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.