## Harmonic Functions and the Mass of 3-Dimensional Asymptotically Flat Riemannian Manifolds

- H. Bray, D. Kazaras, M. Khuri, Daniel L. Stern
- MathematicsJournal of Geometric Analysis
- 15 November 2019

An explicit lower bound for the mass of an asymptotically flat Riemannian 3-manifold is given in terms of linear growth harmonic functions and scalar curvature. As a consequence, a new proof of the… Expand

## Spacetime harmonic functions and the mass of 3-dimensional asymptotically flat initial data for the Einstein equations

- Sven Hirsch, D. Kazaras, M. Khuri
- MathematicsJournal of differential geometry
- 4 February 2020

We give a lower bound for the Lorentz length of the ADM energy-momentum vector (ADM mass) of 3-dimensional asymptotically flat initial data sets for the Einstein equations. The bound is given in… Expand

## Stability of the positive mass theorem under Ricci curvature lower bounds

- D. Kazaras, M. Khuri, Dan A. Lee
- Mathematics
- 9 November 2021

We establish Gromov-Hausdorff stability of the Riemannian positive mass theorem under the assumption of a Ricci curvature lower bound. More precisely, consider a class of orientable complete… Expand

## An explicit formula for spherical curves with constant torsion

- D. Kazaras, I. Sterling
- Mathematics
- 3 October 2012

The purpose of this article is to give an explicit formula for all curves of constant torsion $\tau$ in the unit two-sphere $S^2(1)$. These curves and their basic properties have been known since the… Expand

## ESTIMATE FOR THE ENDANGERED SPECIES EQUATION

- Xiaodong Cao, Mark Cerenzia, D. Kazaras
- Mathematics
- 2014

We prove a differential Harnack inequality for the Endangered Species Equation, which is a nonlinear parabolic equation. Our derivation relies on an idea related to the parabolic maximum principle.… Expand

## Spacetime Harmonic Functions and Applications to Mass

- H. Bray, Sven Hirsch, D. Kazaras, M. Khuri, Yiyue Zhang
- Mathematics
- 22 February 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… Expand

## On positive scalar curvature cobordisms and the conformal Laplacian on end-periodic manifolds

- D. Kazaras, Daniel Ruberman, N. Saveliev
- MathematicsCommunications in analysis and geometry
- 1 February 2019

We show that the periodic $\eta$-invariants introduced by Mrowka--Ruberman--Saveliev~\cite{MRS3} provide obstructions to the existence of cobordisms with positive scalar curvature metrics between… Expand

## Harnack estimate for the Endangered Species Equation

- Xiaodong Cao, Mark Cerenzia, D. Kazaras
- Mathematics
- 26 June 2014

We prove a differential Harnack inequality for the Endangered Species Equation, a nonlinear parabolic equation. Our derivation relies on an idea related to the parabolic maximum principle. As an… Expand

## An intrinsic flat limit of Riemannian manifolds with no geodesics

- J. Basilio, D. Kazaras, C. Sormani
- MathematicsGeometriae Dedicata
- 29 October 2018

In this paper we produce a sequence of Riemannian manifolds $$M_j^m$$ M j m , $$m \ge 2$$ m ≥ 2 , which converge in the intrinsic flat sense to the unit m -sphere with the restricted Euclidean… Expand

## Minimal hypersurfaces and bordism of positive scalar curvature metrics

- B. Botvinnik, D. Kazaras
- Mathematics
- 28 September 2016

Let (Y, g) be a compact Riemannian manifold of positive scalar curvature (psc). It is well-known, due to Schoen–Yau, that any closed stable minimal hypersurface of Y also admits a psc-metric. We… Expand

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