Related papers: Surfaces in which every point sounds the same
We give a geometric condition on a compact subset of a complex manifold which is necessary and sufficient for the existence of a smooth strictly plurisubharmonic function defined in a neighbourhood of this set.
In this paper, we study biharmonic hypersurfaces in Einstein manifolds. Then, we determine all the biharmonic hypersurfaces in irreducible symmetric spaces of compact type which are regular orbits of commutative Hermann actions of…
We study a form of cyclic pursuit on Riemannian manifolds with positive injectivity radius. We conjecture that on a compact manifold, the piecewise geodesic loop formed by connecting consecutive pursuit agents either collapses in finite…
We study the hyperbolicity properties of the action of a non-elementary automorphism group on a compact complex surface, with an emphasis on K3 and Enriques surfaces. A first result is that when such a group contains parabolic elements,…
The Martin boundary of a Cartan-Hadamard manifold describes a fine geometric structure at infinity, which is a sub-space of positive harmonic functions. We describe conditions which ensure that some points of the sphere at infinity belong…
We consider compact K\"ahler manifolds acted on by a connected compact Lie group $K$ of isometries in Hamiltonian fashion. We prove that the squared moment map $\|\mu\|^2$ is constant if and only if the manifold is biholomorphically and…
Every lattice H in a connected semi-simple Lie group G acts properly discontinuously by isometries on the contractible manifold G/K (K a maximal compact subgroup of G). We prove that if H acts on a contractible manifold W and if either 1)…
This paper is connected with the problem of describing path metric spaces that are homeomorphic to manifolds and biLipschitz homogeneous, i.e., whose biLipschitz homeomorphism group acts transitively. Our main result is the following. Let…
Finding a totally geodesic surface, an embedded surface where the geodesics in the surface are also geodesics in the surrounding manifold, has been a problem of interest in the study of 3-manifolds. This has especially been of interest in…
We establish a new criterion for the existence of a global cross section to a non-singular volume-preserving flow on a compact manifold. Namely, if $\Phi$ is a non-singular smooth flow on a compact, connected manifold $M$ with a smooth…
For n bodies moving in Euclidean d-space under the influence of a homogeneous pair interaction we compactify every center-of-mass energy surface, obtaining a 2d(n -1)-1 - dimensional manifold with corners in the sense of Melrose. After a…
We prove a strong multiplicity one theorem for the length spectrum of compact even dimensional hyperbolic spaces i.e. if all but finitely many closed geodesics for two compact even dimensional hyperbolic spaces have the same length, then…
It is proved that an inhomogeneous medium whose boundary contains a weakly singular point of arbitrary order scatters every incoming wave. Similarly, a compactly supported source term with weakly singular points on the boundary always…
Every closed orientable surface S has the following property: any two connected covers of S of the same degree are homeomorphic (as spaces). In this, paper we give a complete classification of compact 3-manifolds with empty or toroidal…
Let (M,g) be a 3-dimensional compact connected real analytic Lorentz manifold and suppose that g is locally homogeneous on a non-empty open set in M (the pseudogroup of local isometries of g has an open orbit). Then we prove that g is…
We consider a magnetic Laplacian on a geometrically finite hyperbolic surface, when the corresponding magnetic field is infinite at the boundary at infinity. We prove that the counting function of the eigenvalues has a particular asymptotic…
With analytical (generalized Mie scattering) and numerical (integral-equation-based) considerations we show the existence of strong resonances in the scattering response of small spheres with lossless impedance boundary. With increasing…
In this paper we investigate the flow of surfaces by a class of symmetric functions of the principal curvatures with a mixed volume constraint. We consider compact surfaces without boundary that can be written as a graph over a sphere. The…
In this paper, we construct a geometrical compactification of the geodesic flow of non-compact complete hyperbolic surfaces $\Sigma$ without cusps having finitely generated fundamental group. We study the dynamical properties of the…
We prove that for any compact manifold of dimension greater than $1$, the set of pseudo-Riemannian metrics having a trivial isometry group contains an open and dense subset of the space of metrics.