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In April 2017 Schoen and Yau posted on the arxiv their solution of the time-symmetric positive mass theorem in all dimensions, which has been a significant conjecture since the 70s. As of now, July 20 …

The positive mass theorem is more or less to do with the geometry of a type of positive scalar curvature condition. Witten's work considers harmonic spinors, which are solutions to a certain linear el …

For any 1-form $\omega$ on a pseudo-Riemannian manifold, the product rule and commutation identity say that $$\omega^p\nabla_p\nabla_q\omega^q-\nabla^q(\omega^p\nabla_p\omega_q)=-\omega^p\omega^qR_{pq …

This is the differential form of the Reilly formula. It holds for a function on any pseudo-Riemannian manifold. (Robert C. Reilly. Applications of the Hessian operator in a Riemannian manifold, Indian …

Is the answer to the following problem, or some close variant thereof, known? Briefly: Given two initial data sets $I_1=(M,g_1,k_1)$ and $I_2=(M,g_2,k_2)$, is there a time-oriented spacetime satisfyi …