Integration by parts and quasi-invariance for the horizontal Wiener measure on foliated compact manifolds

Measure invariance on the Lie-Wiener path space

In this paper we extend some recent results on moment identities, Hermite polynomials, and measure invariance properties on the Wiener space, to the setting of path spaces over Lie groups. In particular we prove the measure invariance of transformations having a quasi-nilpotent covariant derivative via a Girsanov identity and an explicit formula for the expectation of Hermite polynomials in the...

Harmonic bundles on quasi-compact Kähler manifolds

On Kähler manifolds, there exist deep relationships between holomorphic and harmonic objects, between algebraic data and analytic variational principles. For example, through the work of Narasimhan-Seshadri [NS], Donaldson [D1, D2, D3] and Uhlenbeck-Yau [UY] we know that an irreducible holomorphic bundle on a compact Kähler manifold X possesses a Hermite-Einstein (H-E) metric if and only if it ...

LS-categories for foliated manifolds

Classical Integration Rules and Wiener Measure

The Quasi-invariance Property for the Gamma Kernel Determinantal Measure

The Gamma kernel is a projection kernel of the form (A(x)B(y) − B(x)A(y))/(x − y), where A and B are certain functions on the one-dimensional lattice expressed through Euler’s Γfunction. The Gamma kernel depends on two continuous parameters; its principal minors serve as the correlation functions of a determinantal probability measure P defined on the space of infinite point configurations on t...