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ON THE RENORMALIZED VOLUMES FOR CONFORMALLY COMPACT EINSTEIN MANIFOLDS
THE RENORMALIZED VOLUMES CONFORMALLY COMPACT EINSTEIN MANIFOLDS
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2014/4/3
We study the renormalized volume of a conformally compact Einstein manifold. In even dimenions, we derive the analogue of the Chern-Gauss-Bonnet formula incorporating the renormalized volume. When the...
ON THE RENORMALIZED VOLUMES FOR CONFORMALLY COMPACT EINSTEIN MANIFOLDS
ON THE RENORMALIZED VOLUMES CONFORMALLY COMPACT EINSTEIN MANIFOLDS
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2014/4/3
We study the renormalized volume of a conformally compact Einstein manifold. In even dimenions, we derive the analogue of the Chern-Gauss-Bonnet formula incorporating the renormalized volume. When the...
Random determinants, mixed volumes of ellipsoids, and zeros of Gaussian random fields
Gaussian random determinant Wishart matrix Gaussian random parallelotope mixed volumes of ellipsoids location-dispersion ellipsoid
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2012/6/15
Consider a $d\times d$ matrix $M$ whose rows are independent centered non-degenerate Gaussian vectors $\xi_1,...,\xi_d$ with covariance matrices $\Sigma_1,...,\Sigma_d$. Denote by $\mathcal{E}_i$ the ...
Ehrhart polynomials of integral simplices with prime volumes
Integral simplex Ehrhart polynomial δ-vector
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2011/9/20
Abstract: For an integral convex polytope $\Pc \subset \RR^N$ of dimension $d$, we call $\delta(\Pc)=(\delta_0, \delta_1,..., \delta_d)$ its $\delta$-vector and $\vol(\Pc)=\sum_{i=0}^d\delta_i$ its no...
Volumes of chain links
Volumes of chain links Geometric Topology
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2011/9/8
Abstract: Agol has conjectured that minimally twisted n-chain links are the smallest volume hyperbolic manifolds with n cusps, for n at most 10. In his thesis, Venzke mentions that these cannot be sma...
Lower bounds for volumes of nodal sets: an improvement of a result of Sogge-Zelditch
Lower bounds volumes of nodal sets Sogge-Zelditch
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2011/8/22
Abstract: We use the Dong-Sogge-Zelditch formula to obtain a lower bound for the volume of the nodal sets of eigenfunctions. Our result improves the recent results of Sogge-Zelditch and in dimensions ...
Petrov-Galerkin Finite Volumes
Finite volumes mixed finite elements Petrov-Galerkin variational formulation
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2011/1/19
For an elliptic problem with two space dimensions, we propose to formulate the finite volume method with the help of Petrov-Galerkin mixed finite elementsthat are based on the building of a dual Ravia...
Growth of Weil-Petersson volumes and random hyperbolic surfaces of large genus
Growth of Weil-Petersson volumes random hyperbolic surfaces of large genus
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2011/1/20
In this paper, we investigate the geometric properties of hyperbolic surfaces by studying the lengths of simple closed geodesics. The moduli space Mg,n of complete hyperbolic surfaces of genus g ≥ 2 w...
The Isoperimetric Profile of a Noncompact Riemannian Manifold for Small Volumes
Isoperimetric Profile Noncompact Riemannian Manifold for Small Volumes
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2010/11/29
Let M be an n-dimensional Riemannian manifold. We deal, mainly, with the problem of finding a relatively compact domain D ⊂⊂ M that minimizes Area(∂D) among domains of the same volum...
Recurrence interval analysis of trading volumes
Kolmogorov-Smirnov Recurrence interval trading volumes
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2010/4/27
We study the statistical properties of the recurrence intervals $\tau$ between successive trading volumes exceeding a certain threshold $q$. The recurrence interval analysis is carried out for the 20 ...