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In this short note we obtain some gradient estimates for the positive solution to the doubly nonlinear diffusion equation on closed Riemannian manifold with Ricci curvature bounded below by a non-positive constant. As applications, we also derive corresponding Harnack inequalities. [ABSTRACT FROM AUTHOR]

In this article we study surfaces in S3(1) × R for which the R-direction makes a constant angle with the normal plane. We give a complete classification for such surfaces with parallel mean curvature vector. [ABSTRACT FROM AUTHOR]

Abstract: Let Ω be a bounded domain in an n-dimensional Euclidean space . We study eigenvalues of an eigenvalue problem of a system of elliptic equations: Estimates for eigenvalues of the above eigenvalue problem are obtained. Furthermore, we obtain an upper bound on the th eigenvalue . We also obtain sharp lower bound for the first eigenvalue of two kinds of eigenvalue problems of the biharmonic operator on compact manifolds with boundary and positive Ricci curvature. [Copyright &y& Elsevier]

In this paper, we investigate universal inequalities for eigenvalues of the Dirichlet Laplacian and the clamped plate problem on a bounded domain in an n-dimensional polydisk 픻n. Moreover, from the domain monotonicity of the eigenvalue, we can prove that if the first eigenvalue of the Dirichlet Laplacian tends to $\frac n4$ when the domain tends to the polydisk 픻n, then all of the eigenvalues tend to $\frac n4$. [ABSTRACT FROM AUTHOR]

Abstract: For a bounded planar region in , we obtain the ratios of lower order eigenvalues of Laplace operator. Combining our results with the recursive formula in Cheng and Yang (2007) , we can obtain better upper bound of the -th () membrane eigenvalues. [Copyright &y& Elsevier]