Zobrazeno 1 - 10
of 150
pro vyhledávání: '"Ge, Jianquan"'
Autor:
Ge, Jianquan, Zhou, Yi
This is a brief survey of recent results related to austere submanifolds, mainly based on the papers [24,25].
Comment: 14 pages, any comments are welcome
Comment: 14 pages, any comments are welcome
Externí odkaz:
http://arxiv.org/abs/2412.09339
In this paper, following the method of Cheng-Li-Yau, we first modify the coefficients in the constant $B_n$ to improve the volume gap. Further, we also enlarge our gap by applying an estimate of Cheng-Yang for eigenvalues of Laplacian.
Comment:
Comment:
Externí odkaz:
http://arxiv.org/abs/2412.01288
For compact submanifolds in Euclidean and Spherical space forms with Ricci curvature bounded below by a function $\alpha(n,k,H,c)$ of mean curvature, we prove that the submanifold is either isometric to the Einstein Clifford torus, or a topological s
Externí odkaz:
http://arxiv.org/abs/2411.14112
In this paper we give a pinching theorem of the Simon conjecture in the case s=3 and also give a new proof of the cases s=1 and s=2 by some Simons-type integral inequalities.
Comment: 23 pages, accepted by Science China Mathematics
Comment: 23 pages, accepted by Science China Mathematics
Externí odkaz:
http://arxiv.org/abs/2411.03917
In this paper, we establish new normal scalar curvature inequalities on a class of austere submanifolds by proving sharper DDVV-type inequalities on associated austere subspaces. We also provide some examples of austere submanifolds in this class and
Externí odkaz:
http://arxiv.org/abs/2410.17761
In this paper, we give a survey on the history and recent developments on the DDVV-type inequalities.
Comment: any comments are welcome! Accepted by Advances in Mathematics (China)
Comment: any comments are welcome! Accepted by Advances in Mathematics (China)
Externí odkaz:
http://arxiv.org/abs/2402.01085
Autor:
Ge, Jianquan, Zhou, Yi
Motivated by Bryant's research on austere subspaces and Cartan's isoparametric hypersurfaces with 3 distinct principal curvatures, we construct three families of austere submanifolds with flat normal bundle in unit spheres. From these examples we fin
Externí odkaz:
http://arxiv.org/abs/2302.06105
Autor:
Ge, Jianquan, Li, Fagui
For a closed minimal submanifold $f:M^n\looparrowright \mathbb{S}^{N}$ in the unit sphere $(n
Externí odkaz:
http://arxiv.org/abs/2210.04654
We prove that the index is bounded from below by a linear function of its first Betti number for any compact free boundary $f$-minimal hypersurface in certain positively curved weighted manifolds.
Comment: 11 pages, comments are welcome
Comment: 11 pages, comments are welcome
Externí odkaz:
http://arxiv.org/abs/2203.10835
Autor:
Ge, Jianquan, Zhou, Yi
In this paper, we study the existence of constant holomorphic d-scalar curvature and the prescribing holomorphic d-scalar curvature problem on closed, connected almost Hermitian manifolds of dimension $n\geq6$. In addition, we obtain an application a
Externí odkaz:
http://arxiv.org/abs/2202.07913