1 - 9 of 9 articles
We consider versions of Malliavin calculus on path spaces of compact manifolds with diffusion measures, defining Gross–Sobolev spaces of differentiable functions and proving their intertwining with solution maps,
, of certain stochastic differential equations. This is shown to...
We consider simply connected compact Kähler manifolds which have a holomorphic action of a torus group. We use the existing equivariant models for rational homotopy to show that these spaces satisfy an equivariant formality condition over the complex numbers.
Our main objective is to study Hajłasz type Sobolev functions with the exponent one on metric measure spaces equipped with a doubling measure. We show that a discrete maximal function is bounded in the Hajłasz space with the exponent one. This implies that every such function has Lebesgue points...
We consider systems of deformed system of equations, which are obtained by some transformations from the system of incompressible Euler equations. These have similar properties to the original Euler equations including the scaling invariance. For one form of deformed system we prove that finite...
Based on the construction of the discriminant algebra of an even-ranked quadratic form and Rost’s method of shifting quadratic algebras, we give an explicit rational construction of the discriminant algebra of finite-rank algebras and, more generally, of quadratic trace modules, over arbitrary...
We construct quasiconformal mappings in Euclidean spaces by integration of a discontinuous kernel against doubling measures with suitable decay. The differentials of mappings that arise in this way satisfy an isotropic form of the doubling condition. We prove that this isotropic doubling...
We use multiplication maps to give a characteristic-free approach to vanishing theorems on toric varieties. Our approach is very elementary but is enough powerful to prove vanishing theorems.
We study base points of the generalized Θ-divisor on the moduli space of vector bundles on a smooth algebraic curve X of genus g defined over an algebraically closed field. To do so, we use the derived categories Db(Pic0(X)) and Db(Jac(X)) and the equivalence between them given by the...
We study the eigenvalue problems for a class of positive nonlinear operators defined on a cone in a Banach space. Using projective metric techniques and Schauder’s fixed-point theorem, we establish existence, uniqueness, monotonicity and continuity results for the eigensolutions. Moreover, the...
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