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Mass Minimization Problems in General Relativity, pt. 1

Introductory Workshop: New Frontiers in Curvature August 26, 2024 - August 30, 2024

August 26, 2024 (09:30 AM PDT - 10:30 AM PDT)
Speaker(s): Lan-Hsuan Huang (University of Connecticut)
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
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Mass Minimization Problems in General Relativity, pt. 1

Abstract

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The celebrated positive mass theorem, first proven by Schoen and Yau and then by Witten, states that the ADM energy-momentum vector of an asymptotically flat initial data set with the dominant energy condition must be either future timelike or null. This led to a natural conjecture characterizing initial data sets with null ADM energy-momentum, known as the equality case. It turns out that this conjecture is interconnected with the problem of mass minimization in the context of the Bartnik quasi-local mass, known as the stationary conjecture. I will describe a variational approach to advance both conjectures, as well as counterexamples in higher dimensions without the optimal decay rate for asymptotically flatness. These talks are based on a series of joint works with Dan Lee.

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Mass Minimization Problems in General Relativity, pt. 1

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