A generalized Poincaré-Lelong formula

A Generalized Poincaré-lelong Formula and Explicit Green Currents

We prove the following generalization of the classical Poincaré-Lelong formula. Given a holomorphic section f , with zero set Z, of a Hermitian vector bundle E → X , let S be the line bundle over X \Z spanned by f and let Q = E/S. We prove that the Chern form c(DQ) is locally integrable and closed in X and that there is a current W such that ddW = c(DE)− c(DQ)− M, where M is a current with supp...

Some Notes on the Poincaré-Bertrand Formula

Elliptic Complexes and Generalized Poincaré Inequalities

We study first order differential operators P = P(D) with constant coefficients. The main question is under what conditions a generalized Poincaré inequality holds D(f − f 0) L p ≤ C Pf L p , for some f 0 ∈ ker P. We show that the constant rank condition is sufficient, Theorem 3.5. The concept of the Moore-Penrose generalized inverse of a matrix comes into play.

Generalized Schwinger Mass Formula

We generalize Schwinger’s original mass formula to the case of an additional isosinglet which mixes with the nonet mesons, by considering the corresponding 3×3 mass matrix in the most general case. We then make further generalization to either (i) an arbitrary number of additional isosinglets mixing with nonet mesons, or (ii) an arbitrary number of mesons with common J mixing with an additional...

The Generalized Tilt Formula

A convex hull consmaction in Minkowski space defines a canonical cell decomposition for a cusped hyperbolic n-manifold. An algorithm to compute the canonical cell decomposition uses the concept of the 'tilt' of an n-simplex relative to each of its (n 1)-dimensional faces. An essential tool for computing tilts is the tilt theorem. The tilt theorem was previously known only in dimensions n < 3, a...