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Irregular C1,β-Surfaces with an Analytic Metric

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Abstract

We prove that in the class C 1,β with β<1/13 it is possible to continuously deform an analytic convex surface of positive Gaussian curvature (or a plane) so as to lose boundedness of the extrinsic curvature in the Pogorelov sense. We demonstrate how to replace the bound β<1/13 with β<1/7.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk

    Yu. F. Borisov

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  1. Yu. F. Borisov
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Borisov, Y.F. Irregular C1,β-Surfaces with an Analytic Metric. Siberian Mathematical Journal 45, 19–52 (2004). https://doi.org/10.1023/B:SIMJ.0000013011.51242.23

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  • DOI: https://doi.org/10.1023/B:SIMJ.0000013011.51242.23

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