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On singular curves with Gaussian curvature bounds

  • Hao Fang EMAIL logo and Weifeng Wo
Published/Copyright: July 18, 2018

Abstract

In this short note, we consider piece-wise smooth strictly convex curves in 2 with prescribed singular angles. Given some geodesic curvature bounds, we give the sharp length estimates.

Keywords: Singular curve
MSC 2010: 53C42; 49Q10

Funding source: Simons Foundation

Award Identifier / Grant number: 426312

Award Identifier / Grant number: LY16A010002

Award Identifier / Grant number: 11201249

Funding statement: The first author is partially supported by a Simons Foundation research collaboration grant. The second author is supported by the NSFC (no. 11201249) and the Zhejiang Provincial Natural Science Foundation of China (no. LY16A010002).

References

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[3] H. Fang and M. Lai, Gromov Volume of conic 2-spheres, Internat. J. Math. 29 (2018), no. 2, Article ID 1850010. 10.1142/S0129167X18500106Search in Google Scholar

[4] M. Troyanov, Prescribing curvature on compact surfaces with conical singularities, Trans. Amer. Math. Soc. 324 (1991), no. 2, 793–821. 10.1090/S0002-9947-1991-1005085-9Search in Google Scholar

Received: 2017-08-26
Accepted: 2018-05-08
Published Online: 2018-07-18
Published in Print: 2018-08-01

© 2018 Walter de Gruyter GmbH, Berlin/Boston

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