# Spacetime Harmonic Functions and Applications to Mass

@inproceedings{Bray2021SpacetimeHF, title={Spacetime Harmonic Functions and Applications to Mass}, author={Hubert L. Bray and Sven Hirsch and Demetre Kazaras and Marcus A. Khuri and Yiyue Zhang}, year={2021} }

In the pioneering work of Stern [73], level sets of harmonic functions have been shown to be an effective tool in the study of scalar curvature in dimension 3. Generalizations of this idea, utilizing level sets of so called spacetime harmonic functions as well as other elliptic equations, are similarly effective in treating geometric inequalities involving the ADM mass. In this paper, we survey recent results in this context, focusing on applications of spacetime harmonic functions to the…

## 6 Citations

### On a spacetime positive mass theorem with corners

- Mathematics
- 2021

In this paper we consider the positive mass theorem for general initial data sets satisfying the dominant energy condition which are singular across a piecewise smooth surface. We find jump…

### A perturbation of spacetime Laplacian equation

- Mathematics
- 2021

We study a perturbation ∆u+ P |∇u| = h|∇u|, of spacetime Laplacian equation in an initial data set (M,g, p) where P is the trace of the symmetric 2-tensor p and h is a smooth function. Stern [Ste19]…

### The Positive Energy Theorem for Asymptotically Hyperboloidal Initial Data Sets with Toroidal Infinity and Related Rigidity Results

- MathematicsCommunications in Mathematical Physics
- 2022

We establish the positive energy theorem and a Penrose-type inequality for 3-dimensional asymptotically hyperboloidal initial data sets with toroidal infinity, weakly trapped boundary, and satisfying…

### Spectral Torical Band Inequalities and Generalizations of the Schoen-Yau Black Hole Existence Theorem

- Mathematics
- 2023

Generalized torical band inequalities give precise upper bounds for the width of compact manifolds with boundary in terms of positive pointwise lower bounds for scalar curvature, assuming certain…

### Dihedral rigidity for cubic initial data sets

- Mathematics
- 2021

In this paper we pose and prove a spacetime version of Gromov’s dihedral rigidity theorem ([17],[24],[25]) for cubes when the dimension is 3 by studying the level sets of spacetime harmonic functions…

### Hawking Mass Monotonicity for Initial Data Sets

- Mathematics
- 2022

We introduce new systems of PDE on initial data sets $(M,g,k)$ whose solutions model double-null foliations. This allows us to generalize Geroch's monotonicity formula for the Hawking mass under…

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