Journal ArticleDOI
Inequalities for eigenvalues of the drifting Laplacian on Riemannian manifolds
Changyu Xia,Hongwei Xu +1 more
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In this paper, the eigenvalues of the drifting Laplacian on compact Riemannian manifolds with boundary (possibly empty) were studied and a general inequality for them was derived.Abstract:
This paper studies eigenvalues of the drifting Laplacian on compact Riemannian manifolds with boundary (possibly empty) and provides a general inequality for them. Using the general inequality, we obtain universal inequalities for eigenvalues of the drifting Laplacian of Payne-Polya-Weinberger-Yang type for manifolds supporting some special functions. We also obtain a lower bound for the first eigenvalue of the square of the drifting Laplacian on compact manifolds with boundary under some condition on the Bakry-Ricci curvature.read more
Citations
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Evolution and monotonicity of eigenvalues under the Ricci flow
ShouWen Fang,HaiFeng Xu,Peng Zhu +2 more
TL;DR: In this paper, the eigenvalues of the geometric operator were shown to be non-decreasing along the Ricci flow coupled to a heat equation for manifold M with some Ricci curvature condition.
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Estimates for eigenvalues of the bi-drifting Laplacian operator
TL;DR: In this paper, universal inequalities of Payne-Polya-Weinberger-Yang type for eigenvalues of the bi-drifting Laplacian problem on bounded domains in a Euclidean space are obtained.
Journal ArticleDOI
Eigenvalue inequalities for the buckling problem of the drifting Laplacian on Ricci solitons
TL;DR: In this article, the buckling problem of the drifting Laplacian was investigated and a general inequality for its eigenvalues on a bounded connected domain in complete Ricci solitons supporting a special function was obtained.
Journal ArticleDOI
Estimates for eigenvalues of a system of elliptic equations with drift and of bi-drifting laplacian
TL;DR: In this article, the eigenvalue problem of a system of elliptic equations with drift was studied and some universal inequalities of PayneP′olya-Weinberger-Yang type on a bounded domain in Euclidean spaces and inGaussian shrinking solitons.
Journal ArticleDOI
First eigenvalues of geometric operators under the yamabe flow
Shouwen Fang,Fei Yang +1 more
References
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Journal ArticleDOI
Geometry of horospheres
TL;DR: In this article, the authors show that the geometry of horospheres in M may be compared with that in the spaces of constant curvature (a and b) in the Poincare model.
Book ChapterDOI
Isoperimetric and universal inequalities for eigenvalues
TL;DR: A review of the known inequalities for the low eigenvalues of the Dirichlet and Neumann Laplacians on bounded domains in Euclidean space can be found in this paper.
Journal ArticleDOI
On trace identities and universal eigenvalue estimates for some partial differential operators
Evans M. Harrell,Joachim Stubbe +1 more
TL;DR: In this paper, a trace identity for the spectra of self-adjoint operators H modeled on the Dirichlet Laplacian or, more generally, on Schrodinger operators of the form (p−A(x))2 + V (x), where p = 1i ∇ is the usual momentum operator in convenient units and A(x) is the magnetic vector potential.
Journal ArticleDOI
Estimates on Eigenvalues of Laplacian
Qing-Ming Cheng,Hongcang Yang +1 more
TL;DR: In this article, the eigenvalues of Laplacian on a bounded connected domain in an n-dimensional unit sphere Sn(1) or a compact homogeneous Riemannian manifold were studied.