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A note on closed convex hypersurfaces with singularities


Authors: Hao Fang, Mijia Lai and Weifeng Wo
Journal: Proc. Amer. Math. Soc. 147 (2019), 2661-2671
MSC (2010): Primary 53C40
DOI: https://doi.org/10.1090/proc/13886
Published electronically: March 1, 2019
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Abstract: We study closed hypersurfaces in an Euclidean space with point singularities. When certain curvature conditions are prescribed on the smooth part of the hypersurface, we study the geometry of image of the normal map.


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Additional Information

Hao Fang
Affiliation: Department of Mathematics, 14 MacLean Hall, University of Iowa, Iowa City, Iowa 52242
Email: hao-fang@uiowa.edu

Mijia Lai
Affiliation: School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, People’s Republic of China, 200240
Email: laimijia@sjtu.edu.cn

Weifeng Wo
Affiliation: Department of Mathematics, Ningbo University, Ningbo, People’s Republic of China, 315211
Email: woweifeng@nbu.edu.cn

DOI: https://doi.org/10.1090/proc/13886
Received by editor(s): April 10, 2017
Received by editor(s) in revised form: June 8, 2017, and July 9, 2017
Published electronically: March 1, 2019
Additional Notes: The first author was partially supported by a Simons Foundation research collaboration grant.
The second author was partially supported by Shanghai Sailing program No. 15YF1406200 and NSFC No. 11501360.
The third author was supported by the NSFC No. 11201249 and the Zhejiang Provincial Natural Science Foundation of China No. LY16A010002.
Communicated by: Guofang Wei
Article copyright: © Copyright 2019 American Mathematical Society