Science China Mathematics

, Volume 61, Issue 3, pp 511–516 | Cite as

Nonexistence of maximizers for the functional of the centroaffine Minkowski problem

Articles

Abstract

The centroaffine Minkowski problem is studied, which is the critical case of the L p -Minkowski problem. It admits a variational structure that plays an important role in studying the existence of solutions. In this paper, we find that there is generally no maximizer of the corresponding functional for the centroaffine Minkowski problem.

Keywords

centroaffine Minkowski problem Monge-Ampère equation variational structure Blaschke-Santaló inequality 

MSC(2010)

35J96 35J75 53A15 34C40 

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Notes

Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 11401527).

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Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of Applied MathematicsZhejiang University of TechnologyHangzhouChina

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