Related papers: Eigenvalue estimates for submanifolds with locally…

We study a class of Riemannian manifolds which are equipped with a singular metric. In particular we study a domain perturbation problem for the Dirichlet eigenvalues which depends on the best constant in the Hardy Inequality. However, we…

We prove a lower bound for the first Steklov eigenvalue of embedded minimal hypersurfaces with free boundary in a compact $n$-dimensional manifold which has nonnegative Ricci curvature and strictly convex boundary. When $n=3$, this implies…

We prove asymptotically optimal upper bounds for the eigenvalues of the Wentzel-Laplace operator on Riemannian manifolds with Ricci curvature bounded below. These bounds depend highly on the geometry of the boundary in addition to the…

Assuming a lower bound on the Ricci curvature of a complete Riemannian manifold, for $p< 1/2$ we show the existence of bounds on the local $L^p$ norm of the Ricci curvature that depend only on the dimension and which improve with volume…

On compact Riemannian manifolds with non-negative Ricci curvature and smooth (possibly empty), convex (or mean convex) boundary, if the sharp Li-Yau type gradient estimate of an Neumann (or Dirichlet) eigenfunction holds at some…

We generalize previous work on Dirac eigenvalues as dynamical variables of Euclidean supergravity. The most general set of constraints on the curvatures of the tangent bundle and on the spinor bundle of the spacetime manifold under which…

We prove a new lower bound for the first eigenvalue of the Dirac operator on a compact Riemannian spin manifold by refined Weitzenb\"ock techniques. It applies to manifolds with harmonic curvature tensor and depends on the Ricci tensor.…

We study critical Riemannian 4-manifolds with a lower bound on Ricci curvature, but no a priori analytic constraints such as on Sobolev constants. We derive elliptic-type estimates for the local curvature radius, which itself controls…

Under standard local boundary conditions or certain global APS boundary conditions, we get lower bounds for the eigenvalues of the Dirac operator on compact spin manifolds with boundary. Limiting cases are characterized by the existence of…

We establish geometric lower bounds for the smallest positive eigenvalue of the Hodge Laplacian in the class of non-convex domains given by Euclidean annular regions with a convex outer boundary and a spherical inner boundary. These bounds…

We prove qualitative estimates on the total curvature of closed minimal hypersurfaces in closed Riemannian manifolds in terms of their index and area, restricting to the case where the hypersurface has dimension less than seven. In…

We prove a Lichnerowicz type lower bound for the first nontrivial eigenvalue of the $p$-Laplacian on K\"ahler manifolds. Parallel to the $p = 2$ case, the first eigenvalue lower bound is improved by using a decomposition of the Hessian on…

We obtain an estimate for the norm of the second fundamental form of stable H-surfaces in Riemannian 3-manifolds with bounded sectional curvature. Our estimate depends on the distance to the boundary of the surface and on the bounds on the…

We give a curvature dependent lower bound for the filling radius of all closed Riemannian manifolds as well as an upper one for manifolds which are the total space of a Riemannian submersion. The latter applies also to the case of…

In this paper, we study closed four-dimensional manifolds. In particular, we show that under various new pinching curvature conditions (for example, the sectional curvature is no more than 5/6 of the smallest Ricci eigenvalue) then the…

We give lower bounds for the eigenvalues of the submanifold Dirac operator in terms of intrinsic and extrinsic curvature expressions. We also show that the limiting cases give rise to a class generalizing that of Killing spinors. We…

Lieb has shown a lower bound on the smallest Dirichlet eigenvalue of the Laplace operator in terms of a generalized inradius. We derive similar bounds for Robin eigenvalues, for eigenvalues of the polyharmonic operator and the sub-Laplacian…

We prove that the Dirichlet eigenvalues of the Laplace-Beltrami operator on a compact Riemannian manifold with cylindrical boundary can be approximated by the spectrum of truncated graph Laplacians constructed from…

In this paper, we investigate the Dirichlet problem on lower dimensional manifolds for a class of weighted elliptic equations with coefficients that are singular on such sets. Specifically, we study the problem \[\begin{cases} -{\rm…

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.