Dirac and Plateau billiards in domains with corners
By Misha Gromov. 2014
143 citations recorded by the source corpus.
Groping our way toward a theory of singular spaces with positive scalar curvatures we look at the Dirac operator and a generalized Plateau problem in Riemannian manifolds with corners. Using these, we prove that the set of C2-smooth Riemannian metrics g on a smooth manifold X, such that scalg(x) ≥ κ(x), is closed under C0-limits of Riemannian metrics for all continuous functions κ on X. Apart from that our progress is limited but we formulate many conjectures. All along, we emphasize geometry, rather than topology of manifolds with their scalar curvatures bounded from below.
Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/7024939f95d07785c3baca4f6b4b2cbe4baeac00
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Citations in the corpus
- Pointwise lower scalar curvature bounds for $$C^0$$ metrics via regularizing Ricci flow (2019, unknown): “or all t∈ (0,T], so gadmits a uniform approximation by smooth metrics with scalar curvature bounded below by κ. As a corollary of Theorem 1.7, we may answer the following question, posed by Gromov in [8]: Question 1 ([8, Page 1119]). Let g be a continuous Riemannian metric on a closed manifold M whi”
- A Ricci flow proof of a result by Gromov on lower bounds for scalar curvature (2015, methodology): “ we reprove a theorem of Gromov using Ricci flow. The theorem states that a, possibly non-constant, lower bound on the scalar curvature is stable under C0-convergence of the metric. 1. Introduction In [Gro14], Gromovproved the following theorem as an application ofhis theory of singular spaces with p”
- A polyhedron comparison theorem for 3-manifolds with positive scalar curvature (2017, methodology): “umption (1.1) is vacuous, if all the angles j are ˇ=2. In this case, the Euclidean model is a prism with orthogonal base and side faces, and we are able to obtain the prism inequality in section 5.4, [Gro14] as a special case. Motivated by the Schoen-Yau dimension reduction argument [SY79], we have ”