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The uniqueness of the solution in Christoffel and Minkowski problems for open surfaces

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Abstract

We prove uniqueness in the Minkowski problem for open surfaces with spherical image greater than a hemisphere. We extend the class of regions determined earlier by Volkov and the author in which the Christoffel problem has a unique solution.

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Literature cited

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Authors
  1. V. I. Oliker
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Additional information

Translated from Matematicheskie Zametki, Vol. 13, No. 1, pp. 41–49, January, 1973.

In conclusion the author wishes to express his gratitude to Yu. D. Burago, Yu. A. Volkov, and V. G. Maz'e for valuable advice.

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Oliker, V.I. The uniqueness of the solution in Christoffel and Minkowski problems for open surfaces. Mathematical Notes of the Academy of Sciences of the USSR 13, 26–30 (1973). https://doi.org/10.1007/BF01093624

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  • DOI: https://doi.org/10.1007/BF01093624

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