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Mirror symmetric solutions to the centro-affine Minkowski problem

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Abstract

The centro-affine Minkowski problem, a critical case of the \(L_p\)-Minkowski problem in the \(n+1\) dimensional Euclidean space is considered. By applying methods of calculus of variations and blow-up analyses, two sufficient conditions for the existence of solutions to the centro-affine Minkowski problem are established.

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Authors and Affiliations

  1. Department of Mathematics, Tsinghua University, Beijing, 100084, China

    Huaiyu Jian

  2. Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou, 310023, China

    Jian Lu

  3. Department of Mathematics, Tandon School of Engineering, New York University, Six Metrotech, Brooklyn, NY, 11201, USA

    Guangxian Zhu

Authors
  1. Huaiyu Jian
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  2. Jian Lu
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  3. Guangxian Zhu
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Correspondence to Jian Lu.

Additional information

Communicated by N. Trudinger.

The first and second authors were supported by Natural Science Foundation of China (11131005, 11271118, 11401527).

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Jian, H., Lu, J. & Zhu, G. Mirror symmetric solutions to the centro-affine Minkowski problem. Calc. Var. 55, 41 (2016). https://doi.org/10.1007/s00526-016-0976-9

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