Related papers: Volumes of Compact Manifolds

We show that the complex projective space has maximal degree (volume) among all n-dimensional Kahler-Einstein Fano manifolds admitting a holomorphic C^*-action with a finite number of fixed points. The toric version of this result,…

Moduli spaces of compact stable $n$-pointed curves carry a hierarchy of cohomology classes of top dimension which generalize the Weil-Petersson volume forms and constitute a version of Mumford classes. We give various new formulas for the…

We propose an approach to find constant curvature metrics on triangulated closed 3-manifolds using a finite dimensional variational method whose energy function is the volume. The concept of an angle structure on a tetrahedron and on a…

Theorem A. Let $M^n$ denote a closed Riemannian manifold with nonpositive sectional curvature and let $\tilde M^n$ be the universal cover of $M^n$ with the lifted metric. Suppose that the universal cover $\tilde M^n$ contains no totally…

Graph manifolds are manifolds that decompose along tori into pieces with a tame $S^1$-structure. In this paper, we prove that the simplicial volume of graph manifolds (which is known to be zero) can be approximated by integral simplicial…

While studying the existence of closed geodesics and minimal hypersurfaces in compact manifolds, the concept of width was introduced in different contexts. Generally, the width is realized by the energy of the closed geodesics or the volume…

We study the moduli space of M-theories compactified on G_2 manifolds which are asymptotic to a cone over quotients of S^3 x S^3. We show that the moduli space is composed of several components, each of which interpolates smoothly among…

Density estimation is an important technique for characterizing distributions given observations. Much existing research on density estimation has focused on cases wherein the data lies in a Euclidean space. However, some kinds of data are…

The goal of this article is to study compact quasi-Einstein manifolds with boundary. We provide boundary estimates for compact quasi-Einstein manifolds simi\-lar to previous results obtained for static and $V$-static spaces. In addition, we…

We derive an explicit formula for the volume of a regular simplex in the hyperbolic space of any dimension.

We consider a volume maximization program to construct hyperbolic structures on triangulated 3-manifolds, for which previous progress has lead to consider angle assignments which do not correspond to a hyperbolic metric on each simplex. We…

Let $M=G/H$ be a compact connected isotropy irreducible Riemannian homogeneous manifold, where $G$ is a compact Lie group (may be, disconnected) acting on $M$ by isometries. This class includes all compact irreducible Riemannian symmetric…

The class of special generic maps contains Morse functions with exactly two singular points, characterizing spheres topologically which are not $4$-dimensional and the $4$-dimensional unit sphere. This class is for higher dimensional…

Compact quantum metric spaces are order unit spaces along with a Lip norm. On the order unit space of the selfadjoint elements of the dense subalgebra of smooth elements in the quantum Heisenberg manifold we construct Lip norms.

We asymptotically analyse the volume-random variables of general, symmetric and cyclically symmetric plane partitions fitting inside a box. We consider the respective symmetry class equipped with the uniform distribution. We also prove area…

We investigate the topology of the compact submanifolds in round spheres that satisfy a lower bound on the Ricci curvature depending only on the length of the mean curvature vector of the immersion. Just in special cases, the limited…

For an integer $m\geq 1$, a combinatorial manifold $\widetilde{M}$ is defined to be a geometrical object $\widetilde{M}$ such that for $\forall p\in\widetilde{M}$, there is a local chart $(U_p,\phi_p)$ enable $\phi_p:U_p\to…

For closed and oriented hyperbolic surfaces, a formula of Witten establishes an equality between two volume forms on the space of representations of the surface in a semisimple Lie group. One of the forms is a Reidemeister torsion, the…

We develop a general method to calculate entropy numbers of standard Sobolev's classes on an arbitrary compact homogeneous Riemannian manifold. Our method is essentially based on a detailed study of geometric characteristics of norms…

We consider a compact hyperbolic antiprism. It is a convex polyhedron with $2n$ vertices in the hyperbolic space $\mathbb{H}^3$. This polyhedron has a symmetry group $S_{2n}$ generated by a mirror-rotational symmetry of order $2n$, i.e.…