In this paper we prove: if a bounded domain with $C^2$ boundary covers manifold which has finite volume respect to either the Bergman volume, Kähler–Einstein or Kobayashi–Eisenman then is biholomorphic unit ball. This answers question attributed Yau. Further, when convex can assume that only $C^{1,\epsilon}$ regularity.

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In this paper, we are interested in the numerical approximation of the classical time-dependent drift-diffusion system near quasi-neutrality. We consider a fully implicit in time and finite volume in space scheme, where the convection-diffusion fluxes are approximated by ScharfetterGummel fluxes. We establish that all the a priori estimates needed to prove the convergence of the scheme does not...

We consider a simple advection equation in space dimension one and the linearized shallow water equations in space dimension two and describe and implement two different multilevel finite volume discretizations in the context of the utilization of the incremental methods with time explicit or semi-explicit schemes.

There are three main observations which make up the proof. The first observation, discussed in Section 2, is that convex co-compact subgroups of a fundamental group of a hyperbolic 3-manifold N persist in the approximates given by hyperbolic Dehn surgery. This result is stated formally as Proposition 2.1. The second observation, discussed in Section 4, is that a collection of distinct hyperboli...

We show that the aspherical manifolds produced via the relative strict hyperbolization of polyhedra enjoy many group-theoretic and topological properties of open finite volume negatively pinched manifolds, including relative hyperbolicity, nonvanishing of simplicial volume, co-Hopf property, finiteness of outer automorphism group, absence of splitting over elementary subgroups, acylindricity, a...

Let Y\ßf be a finite volume symmetric space with %? the product of half planes. Let A, be the Laplacian on the ¡th half plane, and assume that we have a cusp form , so we have A, = X¡ for i = 1, 2, ... , n . Let A = (Ai,..., An) and let R = \/>-\ + ■ ■ ■ + r2„ with rj + j = A, . Letting r = (ri.rn), we let M(r) denote the dimension of the space of cusp forms with eigenvalue A. More gen...

We apply the finite volume method to a spherically symmetric conservation law of advection-diffusion-reaction type. For the numerical flux we use the so-called complete flux scheme. In this scheme the flux is computed from a local boundary value problem for the complete equation, including the source term. As a result, the numerical flux is the superposition of a homogeneous flux and an inhomog...

A semidiscrete finite volume element(FVE) approximation to parabolic integrodifferential equation(PIDE) is analyzed in a two-dimensional convex polygonal domain. Optimal order L-error estimates are derived for both smooth and nonsmooth initial data. More precisely, for homogeneous equations, an elementary energy technique and duality argument is used to derive optimal L-error estimate of order ...