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A Non-spin Method to the Positive Weighted Mass Theorem for Weighted Manifolds
In this paper, we investigate the weighted mass for weighted manifolds. By establishing a version of density theorem and generalizing Geroch...
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The Case of Equality for the Spacetime Positive Mass Theorem
The rigidity of the spacetime positive mass theorem states that an initial data set ( M , g , k ) satisfying the dominant energy condition with vanishing...
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Density and positive mass theorems for incomplete manifolds
For manifolds with a distinguished asymptotically flat end, we prove a density theorem which produces harmonic asymptotics on the distinguished end,...
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Removable singularity of positive mass theorem with continuous metrics
In this paper, we consider asymptotically flat Riemannian manifolds endowed with a continuous metric and the metric is smooth away from a compact...
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A positive energy theorem for fourth-order gravity
In this paper we prove a positive energy theorem related to fourth-order gravitational theories, which is a higher-order analogue of the classical...
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Mass, Capacitary Functions, and the Mass-to-Capacity Ratio
We study connections among the ADM mass, positive harmonic functions, and capacity of the boundary on asymptotically flat 3-manifolds of nonnegative...
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Desingularizing positive scalar curvature 4-manifolds
We show that the bordism group of closed 3-manifolds with positive scalar curvature (psc) metrics is trivial by explicit methods. Our constructions...
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Generalizations of the Erdős–Kac Theorem and the Prime Number Theorem
In this paper, we study the linear independence between the distribution of the number of prime factors of integers and that of the largest prime...
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Stability of the Spacetime Positive Mass Theorem in Spherical Symmetry
The rigidity statement of the positive mass theorem asserts that an asymptotically flat initial data set for the Einstein equations with zero ADM...
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Mass, center of mass and isoperimetry in asymptotically flat 3-manifolds
We revisit the interplay between the mass, the center of mass and the large scale behavior of certain isoperimetric quotients in the setting of...
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A new proof of Huber’s theorem on differential geometry in the large
In this paper we give a new, and shorter, proof of Huber’s theorem [Theorem 13 in Huber (Comment Math Helve 32:13–72, 1958)] which affirms that for a...
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On the convergence of sequences of positive linear operators towards composition operators
The main aim of the paper is to investigate some sufficient conditions which guarantee the convergence of sequences of positive linear operators...
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Positive Energy Theorems in Fourth-Order Gravity
In this paper we will review some recent results concerning conservation principles associated to higher order gravitational theories. In particular,...