The Spectral Geometry of Einstein Manifolds with Boundary

2003/05/07 by JeongHyeong Park, Park, JeongHyeong
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG #msc:58J50

paper · pdf · doi:10.48550/arxiv.math/0305100

6Pages

arxiv created 2003/05/07 · arxiv updated 2009/11/30

Abstract

Let (M,g) be a compact Einstein manifold with smooth boundary. We consider the spectrum of the p form valued Laplacian with respect to a suitable boundary condition. We show that certain geometric properties of the boundary may be spectrally characterized in terms of this data where we fix the Einstein constant.

Related

• Geometry of Einstein-type manifolds with boundary
• Inverse problems for Einstein manifolds
• The spectral Einstein functional and the noncommutative residue for manifolds with boundary
• Geometry of compact quasi-Einstein manifolds with boundary
• The spectral rigidity of Ricci soliton and Einstein-type manifolds