Kodai Mathematical Journal

Minimal submanifolds with small total scalar curvature in Euclidean space

Keomkyo Seo

Abstract

Let M be an n-dimensional complete minimal submanifold in Rn+p. Lei Ni proved that if M has sufficiently small total scalar curvature, then M has only one end. We improve the upper bound of total scalar curvature. We also prove that if M has the same upper bound of total scalar curvature, there is no nontrivial L2 harmonic 1-form on M.

Article information

Source
Kodai Math. J., Volume 31, Number 1 (2008), 113-119.

Dates
First available in Project Euclid: 25 March 2008

https://projecteuclid.org/euclid.kmj/1206454555

Digital Object Identifier
doi:10.2996/kmj/1206454555

Mathematical Reviews number (MathSciNet)
MR2414237

Zentralblatt MATH identifier
1147.53313

Citation

Seo, Keomkyo. Minimal submanifolds with small total scalar curvature in Euclidean space. Kodai Math. J. 31 (2008), no. 1, 113--119. doi:10.2996/kmj/1206454555. https://projecteuclid.org/euclid.kmj/1206454555