Mean action and the Calabi invariant

Mean Curvature Flow and Bernstein-calabi Results for Spacelike Graphs

This is a survey of our work on spacelike graphic submanifolds in pseudoRiemannian products, namely on Heinz-Chern and Bernstein-Calabi results and on the mean curvature flow, with applications to the homotopy of maps between Riemannian manifolds.

Topologically Left Invariant Mean on Dual Semigroup Algebras

The effective action of N = 1 Calabi - Yau orientifolds

We determine the N = 1 low energy effective action for compactifications of type IIB string theory on compact Calabi-Yau orientifolds in the presence of background fluxes from a Kaluza-Klein reduction. The analysis is performed for Calabi-Yau threefolds which admit an isometric and holomorphic involution. We explicitly compute the Kähler potential, the superpotential and the gauge kinetic funct...

The effective action of Type IIA Calabi-Yau orientifolds

The N = 1 effective action for generic type IIA Calabi-Yau orientifolds in the presence of background fluxes is computed from a Kaluza-Klein reduction. The Kähler potential, the gauge kinetic functions and the flux-induced superpotential are determined in terms of geometrical data of the Calabi-Yau orientifold and the background fluxes. The moduli space is found to be a Kähler subspace of the N...

Invariant Mean Value Property and Harmonic Functions

We give conditions on the functions σ and u on R such that if u is given by the convolution of σ and u, then u is harmonic on R.