Work

Prescribed Ricci curvature near an Einstein manifold with boundary

Year: 2025

Type: article

Abstract: Let ( M , g ) (M,g) be a compact Einstein Riemannian manifold with boundary. We show that under certain conditions, the map that associates to a metric on M M its Ricci curvature, its induced conformal class on the boundary, and its mean curvature on the boundary is locally invertible near g g . The contravariant Ricci operator as well as other operators such as the Einstein operator are also studied.

Source: Proceedings of the American Mathematical Society

DOI: 10.1090/proc/17437

Author: Erwann Delay

Institutions: Centre National de la Recherche Scientifique, Aix-Marseille Université, Laboratoire de Mécanique et d’Acoustique, Laboratoire de Mathématiques d'Avignon

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Agence Nationale de la Recherche

Awards: Orbifolds, scalar curvature and rigidity, Einstein constraints: past, present, and future