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- Title
Metrics with λ1(-Δ+kR)≥0 and Flexibility in the Riemannian Penrose Inequality.
- Authors
Li, Chao; Mantoulidis, Christos
- Abstract
On a closed manifold, consider the space of all Riemannian metrics for which - Δ + k R is positive (nonnegative) definite, where k > 0 and R is the scalar curvature. This spectral generalization of positive (nonnegative) scalar curvature arises naturally for different values of k in the study of scalar curvature via minimal hypersurfaces, the Yamabe problem, and Perelman's Ricci flow with surgery. When k = 1 / 2 , the space models apparent horizons in time-symmetric initial data to the Einstein equations. We study these spaces in unison and generalize Codá Marques's path-connectedness theorem. Applying this with k = 1 / 2 , we compute the Bartnik mass of 3-dimensional apparent horizons and the Bartnik–Bray mass of their outer-minimizing generalizations in all dimensions. Our methods also yield efficient constructions for the scalar-nonnegative fill-in problem.
- Subjects
EINSTEIN, Albert, 1879-1955; RIEMANNIAN manifolds; RICCI flow; CURVATURE; HYPERSURFACES; EINSTEIN field equations; MATHEMATICAL connectedness; GENERALIZATION
- Publication
Communications in Mathematical Physics, 2023, Vol 401, Issue 2, p1831
- ISSN
0010-3616
- Publication type
Article
- DOI
10.1007/s00220-023-04679-9