We review some recent results about the relations among isoperimetric sets, Penrose inequalities and related concepts in the analysis of 3-manifolds of nonnegative scalar curvature. We also show that if the isoperimetric sets of big volume have connected boundaries, the equivalence among suitable notions of mass hold.
Isoperimetric Sets in Nonnegative Scalar Curvature and Their Role Through Various Concepts of Mass / Benatti, Luca; Fogagnolo, Mattia. - 62:(2024), pp. 169-199. ( Anisotropic Isoperimetric Problems & Related Topics Roma 5th September - 9th September 2022) [10.1007/978-981-97-6984-1_8].
Isoperimetric Sets in Nonnegative Scalar Curvature and Their Role Through Various Concepts of Mass
Benatti, Luca;Fogagnolo, Mattia
2024-01-01
Abstract
We review some recent results about the relations among isoperimetric sets, Penrose inequalities and related concepts in the analysis of 3-manifolds of nonnegative scalar curvature. We also show that if the isoperimetric sets of big volume have connected boundaries, the equivalence among suitable notions of mass hold.File in questo prodotto:
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