arXiv subjects

Xingxiao Li

Publications and source records attributed to Xingxiao Li.

23 records · Page 2Linked to original sources

arXiv2013

On the symmetric equiaffine hyperspheres and the minimal symmetric Lagrangian submanifolds

In this paper, a correspondence via duality is established between the set of locally strongly convex symmetric equiaffine hyperspheres and the set of minimal symmetric Lagrangian submanifolds in a certain complex space form. By using this correspondence theorem, we are able to provide an alternative proof of the classification theorem for the locally strongly convex equiaffine hypersurfaces with parallel Fubini-Pick forms, which has been established recently by Z.J. Hu etc in a totally different way.

math.DG↗

arXiv2009

Estimates on eigenvalues for the biharmonic operator on a bounded domain in H^n(-1)

In this paper, we consider eigenvalues of the Dirichlet biharmonic operator on a bounded domain in a hyperbolic space. We obtain universal bounds on the $(k+1)$th eigenvalue in terms of the first $k$th eigenvalue independent of the domains.

math.DG↗

arXiv2009

Universal bounds on eigenvalues of the buckling problem on spherical domains

In this paper we study the eigenvalues of buckling problem on domains in a unit sphere. By introducing a new parameter and using Cauchy inequality, we optimize the inequality obtained by Wang and Xia in [12].

math.DG↗

arXiv2009

Estimates on the first two buckling eigenvalues on spherical domains

In this paper, we study the first two eigenvalues of the buckling problem on spherical domains. We obtain an estimate on the second eigenvalue in terms of the first eigenvalue, which improves one recent result obtained by Wang-Xia in [7].

math.DG↗

arXiv2009

Estimates for the higher order buckling eigenvalues in the unit sphere

We consider the higher order buckling eigenvalues of the following Dirichlet poly-Laplacian in the unit sphere $(-Δ)^p u=Λ(-Δ) u$ with order $p(\geq2)$. We obtain universal bounds on the $(k+1)$th eigenvalue in terms of the first $k$th eigenvalues independent of the domains. In particular, for $p=2$, our result is sharp than estimates on eigenvalues of the buckling problem obtained by Wang and Xia.

math.DG↗