A global pinching theorem for surfaces with constant mean curvature in
Authors:
YiJung Hsu and TaiHo Wang
Journal:
Proc. Amer. Math. Soc. 130 (2002), 157161
MSC (2000):
Primary 53C40, 53C42
Published electronically:
May 3, 2001
MathSciNet review:
1855633
Fulltext PDF Free Access
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Abstract: Let be a compact immersed surface in the unit sphere with constant mean curvature . Denote by the linear map from into , , where is the linear map associated to the second fundamental form and is the identity map. Let denote the square of the length of . We prove that if , then is either totally umbilical or an torus, where is a constant depending only on the mean curvature .
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Additional Information
YiJung Hsu
Affiliation:
Department of Applied Mathematics, National Chiao Tung University, Hsinchu, Taiwan
Email:
yjhsu@math.nctu.edu.tw
TaiHo Wang
Affiliation:
Department of Applied Mathematics, National Chiao Tung University, Hsinchu, Taiwan
Email:
teich@math.sinica.edu.tw
DOI:
http://dx.doi.org/10.1090/S0002993901060300
PII:
S 00029939(01)060300
Keywords:
Mean curvature,
sphere,
totally umbilical
Received by editor(s):
April 17, 1997
Received by editor(s) in revised form:
May 10, 2000
Published electronically:
May 3, 2001
Communicated by:
Christopher Croke
Article copyright:
© Copyright 2001
American Mathematical Society
