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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On the $L_{p}$-Minkowski problem


Authors: Erwin Lutwak, Deane Yang and Gaoyong Zhang
Translated by:
Journal: Trans. Amer. Math. Soc. 356 (2004), 4359-4370
MSC (2000): Primary 52A40
Published electronically: December 15, 2003
MathSciNet review: 2067123
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Abstract: A volume-normalized formulation of the $L_{p}$-Minkowski problem is presented. This formulation has the advantage that a solution is possible for all $p\ge 1$, including the degenerate case where the index $p$ is equal to the dimension of the ambient space. A new approach to the $L_{p}$-Minkowski problem is presented, which solves the volume-normalized formulation for even data and all $p\ge 1$.


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Additional Information

Erwin Lutwak
Affiliation: Department of Mathematics, Polytechnic University, Brooklyn, New York 11201
Email: elutwak@poly.edu

Deane Yang
Affiliation: Department of Mathematics, Polytechnic University, Brooklyn, New York 11201
Email: dyang@poly.edu

Gaoyong Zhang
Affiliation: Department of Mathematics, Polytechnic University, Brooklyn, New York 11201
Email: gzhang@poly.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-03-03403-2
PII: S 0002-9947(03)03403-2
Received by editor(s): May 16, 2001
Received by editor(s) in revised form: April 16, 2003
Published electronically: December 15, 2003
Additional Notes: This research was supported, in part, by NSF Grants DMS–9803261 and DMS–0104363
Article copyright: © Copyright 2003 American Mathematical Society