Related papers: Harmonic Manifolds and Tubes
We establish a min-max estimate on the volume width of a closed Riemannian manifold with nonnegative Ricci curvature. More precisely, we show that every closed Riemannian manifold with nonnegative Ricci curvature admits a PL Morse function…
We develop a general regulated volume expansion for the volume of a manifold with boundary whose measure is suitably singular along a separating hypersurface. The expansion is shown to have a regulator independent anomaly term and a…
The diffusion of particles in confining walls forming a tube is discussed. Such a transport phenomenon is observed in biological cells and porous media. We consider the case in which the tube is winding with curvature and torsion, and the…
We show that every locally flat topological embedding of a 3-manifold in a smooth 5-manifold is homotopic, by a small homotopy, to a smooth embedding. We deduce that topologically locally flat concordance implies smooth concordance for…
In this paper we generalize the main result of [4] for manifolds that are not necessarily Einstein. In fact, we obtain an upper bound for the volume of a locally volume-minimizing closed hypersurface $\Sigma$ of a Riemannian 5-manifold $M$…
This is the second article of a sequence of research on deformations of Q-curvature. In the previous one, we studied local stability and rigidity phenomena of Q-curvature. In this article, we mainly investigate the volume comparison with…
Using a result of Fujita on approximate Zariski decompositions and the singular version of Demailly's holomorphic Morse inequalities as obtained by Bonavero, we express the volume of a line bundle in terms of the absolutely continuous parts…
The stationary points of the total scalar curvature functional on the space of unit volume metrics on a given closed manifold are known to be precisely the Einstein metrics. One may consider the modified problem of finding stationary points…
According to Mostow's celebrated rigidity theorem, the geometry of closed hyperbolic 3-manifolds is already determined by their topology. In particular, the volume of such manifolds is a topological invariant and, as such, has been…
Harmonic analysis on Hermitian symmetric spaces of tube type is a natural framework for introducing multivariate Meixner-Pollaczek polynomials. Their main properties are established in this setting: generating and determinantal formulae,…
In this paper, we give the sharp estimates for the degree of symmetry and the semi-simple degree of symmetry of certain four dimensional fiber bundles by virtue of the rigidity theorem of harmonic maps due to Schoen and Yau. As a corollary…
The main objective of this article is to study the mean curvature flow into an ambient compact smooth manifold M with boundary and with a Riemannian metric that evolves by a self-similar solution of the Ricci flow coupled with the harmonic…
In this paper we determine the topology of three-dimensional complete orientable Riemannian manifolds with a uniform lower bound of sectional curvature whose volume is sufficiently small.
We prove that a strictly stable constant-mean-curvature hypersurface in a smooth manifold of dimension less than or equal to 7 is uniquely homologically area minimizing for fixed volume in a small L^1 neighborhood.
We compute a Simons' type formula for the stress-energy tensor of biharmonic maps from surfaces. Specializing to Riemannian immersions, we prove several rigidity results for biharmonic CMC surfaces, putting in evidence the influence of the…
In this paper, we systematically investigate the geometry and topology of manifolds with integral radial curvature bounds, and obtain many interesting and important conclusions.
Multivariate normal mixtures provide a flexible method of fitting high-dimensional data. It is shown that their topography, in the sense of their key features as a density, can be analyzed rigorously in lower dimensions by use of a…
The functionality of proteins is related to their structure in the native state. Protein structures are made up of emergent building blocks of helices and almost planar sheets. A simple coarse-grained geometrical model of a flexible tube…
We discuss the response of thin cylindrical tubes to small indentations. The stretching-free embedding of these surfaces is completely determined by the embedding of one edge curve, thus reducing their bending response to an effectively one…
The Lichnerowicz conjecture asserts that all harmonic manifolds are either flat or locally symmetric spaces of rank 1. This conjecture has been proved by Z.I. Szabo for harmonic manifolds with compact universal cover. E. Damek and F. Ricci…