15 citations · 29 across the 19 of their papers we have counts for
21 papers
The Positive Mass Theorem for Creased Initial Data
Demetre Kazaras, Marcus Khuri, Michael Lin
We establish a spacetime positive mass theorem and rigidity statement for asymptotically flat spin initial data sets with a codimension one singularity controlled by a matching Bar…
Proof of the Spacetime Penrose Inequality With Suboptimal Constant in the Asymptotically Flat and Asymptotically Hyperboloidal Regimes
Brian Allen, Edward Bryden, Demetre Kazaras +1
We establish mass lower bounds of Penrose-type in the setting of -dimensional initial data sets for the Einstein equations satisfying the dominant energy condition, which are ei…
Codimension 2 drawstrings with scalar curvature lower bounds
Demetre Kazaras, Kai Xu
We produce new examples of Riemannian manifolds with scalar curvature lower bounds and collapsing behavior along codimension 2 submanifolds. Applications of this construction are g…
Scalar curvature and volume entropy of hyperbolic 3-manifolds
Demetre Kazaras, Antoine Song, Kai Xu
We show that any closed hyperbolic 3-manifold M admits a Riemannian metric with scalar curvature at least -6, but with volume entropy strictly larger than 2. In particular, this co…
Drawstrings and flexibility in the Geroch conjecture
Demetre Kazaras, Kai Xu
In this paper, we observe new phenomena related to the structure of 3-manifolds satisfying lower scalar curvature bounds. We construct warped-product manifolds of almost nonnegativ…
On the Stability of Llarull's Theorem in Dimension Three
Brian Allen, Edward Bryden, Demetre Kazaras
Llarull's Theorem states that any Riemannian metric on the -sphere which has scalar curv{\-}ature greater than or equal to , and whose distance function is bounded below…
Spectral Torical Band Inequalities and Generalizations of the Schoen-Yau Black Hole Existence Theorem
Sven Hirsch, Demetre Kazaras, Marcus Khuri +1
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, a…
Stability of the positive mass theorem and torus rigidity theorems under integral curvature bounds
Brian Allen, Edward Bryden, Demetre Kazaras
Work of D. Stern and Bray-Kazaras-Khuri-Stern provide differential-geometric identities which relate the scalar curvature of Riemannian 3-manifolds to global invariants in terms of…
Rigid comparison geometry for Riemannian bands and open incomplete manifolds
Sven Hirsch, Demetre Kazaras, Marcus Khuri +1
Comparison theorems are foundational to our understanding of the geometric features implied by various curvature constraints. This paper considers manifolds with a positive lower b…
Stability of the positive mass theorem under Ricci curvature lower bounds
Demetre Kazaras, Marcus Khuri, Dan Lee
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 orientabl…
Spacetime Harmonic Functions and Applications to Mass
Hubert Bray, Sven Hirsch, Demetre Kazaras +2
In the pioneering work of Stern, 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 i…
Spacetime Harmonic Functions and the Mass of 3-Dimensional Asymptotically Flat Initial Data for the Einstein Equations
Sven Hirsch, Demetre Kazaras, Marcus Khuri
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 bou…
Harmonic Functions and The Mass of 3-Dimensional Asymptotically Flat Riemannian Manifolds
Hubert L. Bray, Demetre P. Kazaras, Marcus A. Khuri +1
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…
Smocked Metric Spaces and their Tangent Cones
Christina Sormani, Demetre Kazaras, David Afrifa +11
We introduce the notion of a smocked metric spaces and explore the balls and geodesics in a collection of different smocked spaces. We find their rescaled Gromov-Hausdorff limits a…
Desingularizing positive scalar curvature 4-manifolds
Demetre Kazaras
We show that the bordism group of closed 3-manifolds with positive scalar curvature (psc) metrics is trivial by explicit methods. Our constructions are derived from scalar-flat K{ä…
On positive scalar curvature cobordisms and the conformal Laplacian on end-periodic manifolds
Demetre Kazaras, Daniel Ruberman, Nikolai Saveliev
We show that the periodic -invariants introduced by Mrowka--Ruberman--Saveliev~\cite{MRS3} provide obstructions to the existence of cobordisms with positive scalar curvature met…
An intrinsic flat limit of Riemannian manifolds with no geodesics
Jorge Basilio, Demetre Kazaras, Christina Sormani
In this paper we produce a sequence of Riemannian manifolds , , which converge in the intrinsic flat sense to the unit -sphere with the restricted Euclidean dist…
Minimal hypersurfaces and bordism of positive scalar curvature metrics
Boris Botvinnik, Demetre Kazaras
Let 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 also admits…
Gluing Scalar-Flat Manifolds with Vanishing Mean Curvature on the Boundary
Demetre Kazaras
We establish a gluing theorem for solutions of a Yamabe problem for manifolds with boundary studied by Escobar in the 90's. Given two scalar-flat Riemannian manifolds whose boundar…
Harnack Estimate for the Endangered Species Equation
Xiaodong Cao, Mark Cerenzia, Demetre Kazaras
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 pr…
An Explicit Formula for the Spherical Curves with Constant Torsion
Demetre Kazaras, Ivan Sterling
The purpose of this article is to give an explicit formula for all curves of constant torsion in the unit two-sphere . These curves and their basic properties have been…