Ricci decomposition

About: Ricci decomposition is a research topic. Over the lifetime, 1972 publications have been published within this topic receiving 45295 citations.

Left-Degenerate Vacuum Metrics

Abstract: For all complex space-times in which the self-dual part of the Weyl tensor is algebraically degenerate, Einstein's vacuum equations are reduced to a single differential equation of the second order and second degree.

Proper generalized decomposition for nonlinear convex problems in tensor Banach spaces

Abstract: Tensor-based methods are receiving a growing interest in scientific computing for the numerical solution of problems defined in high dimensional tensor product spaces. A family of methods called proper generalized decompositions (PGD) methods have been recently introduced for the a priori construction of tensor approximations of the solution of such problems. In this paper, we give a mathematical analysis of a family of progressive and updated PGDs for a particular class of problems associated with the minimization of a convex functional over a reflexive tensor Banach space.

A Liouville-Type Theorem for Smooth Metric Measure Spaces

Abstract: For smooth metric measure spaces (M,g,e −f d vol ) we prove a Liouville-type theorem when the Bakry–Emery Ricci tensor is nonnegative. This generalizes a result of Yau, which is recovered in the case f is constant. This result follows from a gradient estimate for f-harmonic functions on smooth metric measure spaces with Bakry–Emery Ricci tensor bounded from below.