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of 141
pro vyhledávání: '"Ge, Jianquan"'
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 immersed minimal submanifold $M^n$ in the unit sphere $\mathbb{S}^{N}$ $(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
Autor:
Chen, Niang, Ge, Jianquan
In this paper, via a new Hardy type inequality, we establish some cohomology vanishing theorems for free boundary compact submanifolds $M^n$ with $n\geq2$ immersed in the Euclidean unit ball $\mathbb{B}^{n+k}$ under one of the pinching conditions $|\
Externí odkaz:
http://arxiv.org/abs/2106.05793
Autor:
Ge, Jianquan, Li, Fagui
We prove a weak version of the Perdomo Conjecture, namely, there is a positive constant $\delta(n)>0$ depending only on $n$ such that on any closed embedded, non-totally geodesic, minimal hypersurface $M^n$ in $\mathbb{S}^{n+1}$, $$\int_{M}S \geq \de
Externí odkaz:
http://arxiv.org/abs/2103.07747
In order to study the Yamabe changing-sign problem, Bahri and Xu proposed a conjecture which is a universal inequality for $p$ points in $\mathbb R^m$. They have verified the conjecture for $p\leq3$. In this paper, we first simplify this conjecture b
Externí odkaz:
http://arxiv.org/abs/2101.10023
Autor:
Ge, Jianquan, Li, Fagui
Combining the intrinsic and extrinsic geometry, we generalize Einstein manifolds to Integral-Einstein (IE) submanifolds. A Takahashi-type theorem is established to characterize minimal hypersurfaces with constant scalar curvature (CSC) in unit sphere
Externí odkaz:
http://arxiv.org/abs/2101.03753
Autor:
Ge, Jianquan
We prove an old conjecture of S. S. Chern that the Euler characteristic of a closed affine manifold equals to zero.
Comment: There is a minor error in the Hessian representation in Lemma 2.1. found by Andrea Clini on February 17 (I was aware of
Comment: There is a minor error in the Hessian representation in Lemma 2.1. found by Andrea Clini on February 17 (I was aware of
Externí odkaz:
http://arxiv.org/abs/2002.03105