相关论文: Crofton formulae for products
We introduce a simple procedure to integrate differential forms with arbitrary holomorphic poles on Riemann surfaces. It gives rise to an intrinsic regularization of such singular integrals in terms of the underlying conformal geometry.…
Several formulations have long existed in the literature in the form of continuous mixtures of normal variables where a mixing variable operates on the mean or on the variance or on both the mean and the variance of a multivariate normal…
The matrix integral has many applications in diverse fields. This review article begins by presenting detailed key background knowledge about matrix integral. Then the volumes of orthogonal groups and unitary groups are computed,…
Generalized differential forms are used in discussions of metric geometries and Einstein's vacuum field equations. Cartan's structure equations are generalized and applied. In particular flat generalized connections are associated with any…
We obtain integral formulas for a metric-affine space equipped with two complementary orthogonal distributions. The integrand depends on the Ricci and mixed scalar curvatures and invariants of the second fundamental forms and integrability…
This paper extends our earlier results to higher dimensions using a different approach, based on the rigidity of complex structures on certain domains.
Generalized trigonometric functions are applied to the Legendre-Jacobi standard form of complete elliptic integrals, and a new form of the generalized complete elliptic integrals of the Borweins is presented. According to the form, it can…
Intrigued by the product formula prod_{i=1}^{n-2} C_i for the volume of the Chan-Robbins-Yuen polytope CRY_n, where C_i is the ith Catalan number, we construct a family of polytopes P_{m,n}, whose volumes are given by the product…
By some hypergeometric summation theorems, the authors establish a series of new infinite summation formulas involving generalized harmonic numbers related to Riemann-Zeta function, with three different patterns.
In earlier work, we have developed a nonequilibrium statistical field theory description of cosmic structure formation, dubbed Kinetic Field Theory (KFT), which is based on the Hamiltonian phase-space dynamics of classical particles and…
A mathematical framework of cohomological field theories (CohFTs) is formulated in the language of bigraded manifolds. Algebraic properties of operators in CohFTs are studied. Methods of constructing CohFTs, with or without gauge…
Generalizing Weyl's tube formula and building on Chern's work, Alesker reinterpreted the Lipschitz-Killing curvature integrals as a family of valuations (finitely-additive measures with good analytic properties), attached canonically to any…
The purpose of this note is to provide some volume estimates for Einstein warped products similar to a classical result due to Calabi and Yau for complete Riemannian manifolds with nonnegative Ricci curvature. To do so, we make use of the…
We prove that a Poisson-Newton formula, in a broad sense, is associated to each Dirichlet series with a meromorphic extension to the whole complex plane. These formulas simultaneously generalize the classical Poisson formula and Newton…
A class of trigonometric integrator is proposed for the constrained ring polymer Hamiltonian dynamics, arising from the path integral molecular dynamics. The integrator is formulated by the composition of flows, thereby integrating the…
In this article, we deduce a series of integral formulas for a foliated sub-Riemannian manifold, which is a new geometric concept denoting a Riemannian manifold equipped with a distribution ${\mathcal D}$ and a foliation ${\mathcal F}$,…
We consider generalized gravitational entropy in various higher derivative theories of gravity dual to four dimensional CFTs using the recently proposed regularization of squashed cones. We derive the universal terms in the entanglement…
An alternative derivation of generalized gravitational entropy associated to co-dimension 2 'entangling' hypersurfaces is given. The approach is similar to the Jacobson-Myers 'Hamiltonian' method and it does not require computations on…
We extend the Neumann's methods and give the explicit formulae for the volume and the Chern-Simons invariant for hyperbolic alternating knot orbifolds.
The morphometric approach is a powerful ansatz for decomposing the chemical potential for a complex solute into purely geometrical terms. This method has proven accuracy in hard spheres, presenting an alternative to comparatively expensive…