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Prescribing gaussian curvatures on surfaces with conical singularities

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Abstract

We consider prescribing Gaussian curvatures on surfaces with conical singularities. In a critical case, we obtain the best constant in an inequality. Then, by using the “distribution of mass” analysis, we are able to provide some sufficient conditions for a function to be the Gaussian curvature of some pointwise conformai metric.

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Authors and Affiliations

  1. Department of Mathematics, University of Arizona, 85721, Tuscon, AZ, USA

    Wenxiong Chen & Congming Li

  2. Department of Mathematics, University of Pennsylvania, 19104, Philadelphia, PA, USA

    Wenxiong Chen & Congming Li

Authors
  1. Wenxiong Chen
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  2. Congming Li
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Additional information

Communicated by Jerry Kazdan

Partially supported by NSF Grant DMS-9003694.

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Chen, W., Li, C. Prescribing gaussian curvatures on surfaces with conical singularities. J Geom Anal 1, 359–372 (1991). https://doi.org/10.1007/BF02921311

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  • DOI: https://doi.org/10.1007/BF02921311

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