By Topic

Scalar curvature of hypersurfaces with constant mean curvature in spheres

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

The purchase and pricing options are temporarily unavailable. Please try again later.
1 Author(s)
Haizhong, Li ; Department of Applied Mathematics, Tsinghua University, Beijing 100084

LetM be a closed hypersurface with constantmean curvature H in a unit sphere space Sn+1, n ≤ 5, and S the square of the length of the second fundamental form of M. If | H | < ∈ (n), then there exists δ(n, H) > 0 such that if $n+(n^{3})/(n-1)H^{2}+(n(n-2))/(2(n-1))sqrt{n^{2}H^{4}+4(n-1)H^{2}}leq S leq n + (n^{3})/(2(n-1))H^{2}+(n(n-2))/(2(n-1))times sqrt{n^{2}H^{4}+4(n-1)H^{2}}+delta (n, H)$, then $Sequiv n+ (n^{3})/(2(n-1))H^{2}+(n(n-2))/(2(n-1))sqrt{n^{2}H^{4}+(n-1)H^{2}}$ and these hypersurfaces are determined, where ∈ (n) is a constant depending only on n. In the case H ≡ 0, Peng-Terng ts result is recovered.

Published in:

Tsinghua Science and Technology  (Volume:1 ,  Issue: 3 )