Laplace operatorFirst eigenvalueSpherical unitary representationLow rank representationAutomorphic representationThis paper is concerned with the lower bound for the first positive eigenvalue of the Laplace operator on the space of square integrable functions on some locally symmetric space , where , is a...
In this paper, we derive the evolution equation for the eigenvalues of p-Laplace operator. Moreover, we show the following main results. Let ( ${M^{n}, g(t)), t\in [0,T),}$ be a solution of the unnormalized powers of the mth mean curvature flow on a closed manifold and λ1,...
Let (M,g) be an n-dimensional closed Riemannian manifold with the Ricci curvature bounded from below. In the present paper we get the lower bound of the fi
Let (M,g) be an n-dimensional closed Riemannian manifold with the Ricci curvature bounded from below. In the present paper we get the lower bound of the fi
First eigenvalue for the p-Laplace operator Nonlinear Anal. (2000) D. Valtorta Sharp estimate on the first eigenvalue of the p-Laplacian Nonlinear Anal. (2012) B. Andrews Pinching estimates and motion of hypersurfaces by curvature functions J. Reine Angew. Math. (2007) H. Bray Proof of th...
1.A Discussion of the Lower Bound on the First Eigenvalue of Sturm-Liouville Problem;关于SL问题的第一特征值的下界讨论 2.Estimate of the First Eigenvalue on Compact Manifolds紧致黎曼流形第一特征值下界的估计 3.The First Eigenvalue of the Laplace Operator Under the Yamabe FlowYamabe流上的Laplace...
We study the Steklov eigenvalue problem for the ∞-orthotropic Laplace operator defined on convex sets of RN, with N≥2, considering the limit for p→+∞ of the Steklov problem for the p-orthotropic Laplacian. We find a limit problem that is satisfied in the viscosity sense and a geometric...
1.Introductionandstatementofmainresults AmongallthepossibleRiemannianmetricsonacompactdifferentiable manifoldM,themostinterestingonesarethosewhichextremizeagiven Riemannianinvariant.Inparticular,manyrecentworkshavebeendevoted tothemetricswhichmaximizethefundamentaleigenvalueλ 1 (M,g)ofthe Laplace-Beltramioperator...
In this paper, we first give a short review of the eigenvalue estimates of Laplace operator and Schrdinger operators. Then we discuss the evolution of eigenvalues along the Ricci flow, and two new bounds of the first eigenvalue using gradient estimates. 2000 Mathematics Subject Classification: 58...
and some special pinching conditions on the second fundamental form of the initial hypersurface, we prove that the first nonzero closed eigenvalues of the Laplace operator and the p-Laplace operator are monotonic under the forced MCF, respectively, which partially generalize Mao and Zhao’s work. ...