In this paper, we derive from the supersymmetry of the Witten Laplacian Brascamp-Lieb’s type inequalities for general differential forms on compact Riemannian manifolds with boundary. In addition to the supersymmetry, our results essentially follow from suitable decompositions of the quadratic forms associated with the Neumann and Dirichlet self-adjoint realizations of the Witten Laplacian. The...

In this work, we construct the non-relativistic Lee model on some class of three dimensional Riemannian manifolds by following a novel approach introduced by S. G. Rajeev [1]. This approach together with the help of heat kernel allows us to perform the renormalization non-perturbatively and explicitly. For completeness, we show that the ground state energy is bounded from below for different cl...

We construct infinite families of regular normal Cartan geometries with nonvanishing curvature and essential automorphisms on closed manifolds for many higher rank parabolic model geometries. To do this, we use particular elements the kernel Kostant Laplacian to homogeneous desired type, giving a global realization an elegant local construction due Kruglikov The, then modify these make their ba...

1. The main result and some consequences. In 1956 E. Calabi [6] attacked the classification problem of compact euclidean space forms by means of a special construction, called the Calabi construction (see Wolf [14, p. 124]). Here we announce that the construction can be extended to compact riemannian manifolds whose Ricci curvature tensor is zero (Ricci flat). Of course, it is not known if ther...

(0.0) For projective curves,there exists a fundamental dichotomy between curves of genus 0 or 1 on one side, and curves of genus 2 or more on the other side.This dichotomy appears at many levels, such as: Kodaira dimension, topology (fundamental group), hyperbolicity properties (as expressed by the Kobayashi pseudo-metric), and arithmetic geometry (see [La 1,2] and section 7 below). The objecti...

In this paper the perfect Morse functions on a compact manifold are studied. Some constructions of such functions on compact manifolds and some applications are also given.

Twistor forms are a natural generalization of conformal vector fields on Riemannian manifolds. They are defined as sections in the kernel of a conformally invariant first order differential operator. We study twistor forms on compact Kähler manifolds and give a complete description up to special forms in the middle dimension. In particular, we show that they are closely related to Hamiltonian 2...

We study Hamiltonian dynamics of gradient Kähler-Ricci solitons that arise as limits of dilations of singularities of the Ricci flow on compact Kähler manifolds. Our main result is that the underlying spaces of such gradient solitons must be Stein manifolds. Moreover, on all most all energy surfaces of the potential function f of such a soliton, the Hamiltonian vector field Vf of f , with respe...