4 papers
Heat kernel geometry and Gromov's volume growth conjecture
Jian Ge
In 1986, Gromov asked whether every complete noncompact -dimensional Riemannian manifold with nonnegative Ricci curvature and scalar curvature at least one satisfies: \[ \Vol_g…
Normal-Yang-Mills and Tangent-Yang-Mills submanifolds
Jianquan Ge, Lixin Xiao, Wenjin Zhang
This paper investigates the variational problems associated with the -norms of the normal and tangent curvature tensors for submanifolds immersed in a unit sphere. We define t…
Complete hypersurfaces in with constant mean and scalar curvature
Jianquan Ge, Ya Tao
In this paper, we investigate the rigidity problems of complete hypersurfaces with constant mean curvature and constant scalar curvature in Euclidean spaces. Firstly, under some co…
Chern Conjecture on Minimal Willmore Hypersurfaces with Constant Scalar Curvature
Jianquan Ge, Huixin Tan, Wenjiao Yan +1
In this paper, we prove that for an -dimensional closed minimal Willmore hypersurface with constant scalar curvature in the unit sphere , the squared nor…