Polar Transform of Conformally Flat Metrics

Polar Transform of Conformally Flat Metrics In the theory of convex subsets in a Euclidean space, an important role is played by Minkowski duality (the polar transform of a convex set, or the Legendre transform of a convex set). We consider conformally flat Riemannian metrics on the n-dimensional unit sphere and their embeddings into the isotropic cone of the Lorentz space. For a given class of metrics, we define and carry out a detailed study of the Legendre transform. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Siberian Advances in Mathematics Springer Journals

Polar Transform of Conformally Flat Metrics

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Allerton Press, Inc.
Subject
Mathematics; Mathematics, general
ISSN
1055-1344
eISSN
1934-8126
D.O.I.
10.3103/S1055134418020025
Publisher site
See Article on Publisher Site

Abstract

In the theory of convex subsets in a Euclidean space, an important role is played by Minkowski duality (the polar transform of a convex set, or the Legendre transform of a convex set). We consider conformally flat Riemannian metrics on the n-dimensional unit sphere and their embeddings into the isotropic cone of the Lorentz space. For a given class of metrics, we define and carry out a detailed study of the Legendre transform.

Journal

Siberian Advances in MathematicsSpringer Journals

Published: May 30, 2018

References

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