In this paper, a new proof of the Positive Mass Theorem is established through a newly discovered monotonicity formula, holding along the level sets of the Green’s function of an asymptotically flat 3-manifolds. In the same context and for 1 < p < 3, a Geroch-type calculation is performed along the level sets of p-harmonic functions, leading to a new proof of the Riemannian Penrose Inequality under favourable assumptions. A new characterisation of scalar curvature lower bounds in terms of the monotonicity formulas is also given.
A Green’s Function Proof of the Positive Mass Theorem / Agostiniani, Virginia; Mazzieri, Lorenzo; Oronzio, Francesca. - In: COMMUNICATIONS IN MATHEMATICAL PHYSICS. - ISSN 0010-3616. - 405:2(2024), pp. 5401-5423. [10.1007/s00220-024-04941-8]
A Green’s Function Proof of the Positive Mass Theorem
Agostiniani, Virginia;Mazzieri, Lorenzo;Oronzio, Francesca
2024-01-01
Abstract
In this paper, a new proof of the Positive Mass Theorem is established through a newly discovered monotonicity formula, holding along the level sets of the Green’s function of an asymptotically flat 3-manifolds. In the same context and for 1 < p < 3, a Geroch-type calculation is performed along the level sets of p-harmonic functions, leading to a new proof of the Riemannian Penrose Inequality under favourable assumptions. A new characterisation of scalar curvature lower bounds in terms of the monotonicity formulas is also given.File | Dimensione | Formato | |
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