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Transactions of the American Mathematical Society
ISSN 1088-6850(e) ISSN 0002-9947(p)

     

On the $L_{p}$-Minkowski problem

Author(s): Erwin Lutwak; Deane Yang; Gaoyong Zhang
Journal: Trans. Amer. Math. Soc. 356 (2004), 4359-4370.
MSC (2000): Primary 52A40
Posted: December 15, 2003
MathSciNet review: 2067123
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Abstract | References | Similar articles | Additional information

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: 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
Posted: December 15, 2003
Additional Notes: This research was supported, in part, by NSF Grants DMS--9803261 and DMS--0104363
Copyright of article: Copyright 2003, American Mathematical Society




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