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## Publications of Demetre P Kazaras    :chronological  alphabetical  combined listing:

%% Papers Published
@article{fds354055,
Author = {Basilio, J. and Kazaras, D. and Sormani, C.},
Title = {An intrinsic flat limit of Riemannian manifolds with no
geodesics},
Journal = {Geom. Dedicata},
Volume = {204},
Pages = {265-284},
Year = {2020},
Abstract = {In this paper we produce a sequence of Riemannian manifolds
M^m_j, m≥2, which converge in the intrinsic flat sense to
the unit m-sphere with the restricted Euclidean distance.
This limit space has no geodesics achieving the distances
between points, exhibiting previously unknown behavior of
intrinsic flat limits. In contrast, any compact
Gromov–Hausdorff limit of a sequence of Riemannian
manifolds is a geodesic space. Moreover, if m≥3, the
manifolds M^m_j may be chosen to have positive scalar
curvature.},
Key = {fds354055}
}

@article{fds354054,
Author = {Botvinnik, Boris and Kazaras, Demetre},
Title = {Minimal hypersurfaces and bordism of positive scalar
curvature metrics},
Journal = {Math. Ann.},
Volume = {371},
Number = {1-2},
Pages = {189-224},
Year = {2018},
Abstract = {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 establish an analogous result
for stable minimal hypersurfaces with free boundary.
Furthermore, we combine this result with tools from
geometric measure theory and conformal geometry to study
psc-bordism. For instance, assume (Y_0,g_0) and (Y_1,g_1)
are closed psc-manifolds equipped with stable minimal
hypersurfaces X_0 \subset Y_0 and X_1\subset Y_1. Under
natural topological conditions, we show that a psc-bordism
(Z,{\bar{g}}) : (Y_0,g_0)\rightsquigarrow (Y_1,g_1) gives
rise to a psc-bordism between X_0 and X_1 equipped with the
psc-metrics given by the Schoen–Yau construction.},
Key = {fds354054}
}

@article{fds354053,
Author = {Demetre Kazaras},
Title = {Gluing Manifolds with Boundary and Bordisms of Positive
Scalar Curvature Metrics},
Journal = {(Thesis -- University of Oregon)},
Year = {2017},
Abstract = {This thesis presents two main results on analytic and
topological aspects of scalar curvature. The first is a
gluing theorem for scalar-flat manifolds with vanishing mean
curvature on the boundary. Our methods involve tools from
conformal geometry and perturbation techniques for nonlinear
elliptic PDE. The second part studies bordisms of positive
scalar curvature metrics. We present a modification of the
Schoen-Yau minimal hypersurface technique to manifolds with
boundary which allows us to prove a hereditary property for
bordisms of positive scalar curvature metrics. The main
technical result is a convergence theorem for stable minimal
hypersurfaces with free boundary in bordisms with long
collars which may be of independent interest.},
Key = {fds354053}
}

@article{fds354052,
Author = {Cao, Xiaodong and Cerenzia, Mark and Kazaras, Demetre},
Title = {Harnack estimate for the endangered species
equation},
Journal = {Proc. Amer. Math. Soc.},
Volume = {143},
Number = {10},
Pages = {4537–4545},
Year = {2015},
Abstract = {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. As an application of this
inequality, we will show that positive solutions to this
equation must blow up in finite time.},
Key = {fds354052}
}

@article{fds354051,
Author = {Demetre Kazaras and Ivan Sterling},
Title = {An explicit formula for spherical curves with constant
torsion},
Journal = {Pacific J. Math.},
Volume = {259},
Number = {2},
Pages = {361-372},
Year = {2012},
Month = {Summer},
ISSN = {0030-8730},
Abstract = {We give an explicit formula for all curves of constant
torsion in the unit two-sphere. Our approach uses
hypergeometric functions to solve relevant ordinary
differential equations.},
Key = {fds354051}
}

%% Papers Accepted
@article{fds354056,
Author = {D. Kazaras and D. Ruberman and N. Saveliev},
Title = {On positive scalar curvature cobordisms and the conformal
Laplacian on end-periodic manifolds},
Journal = {Communications in Analysis and Geometry},
Volume = {to appear, accepted 2019},
Year = {2020},
Abstract = {We show that the periodic η-invariants introduced by
Mrowka--Ruberman--Saveliev~\cite{MRS3} provide obstructions
to the existence of cobordisms with positive scalar
curvature metrics between manifolds of dimensions 4 and 6.
The proof combines a relative version of the Schoen--Yau
minimal surface technique with an end-periodic index theorem
for the Dirac operator. As a result, we show that the
bordism groups Ω^{spin,+}_{n+1}(S1×BG) are infinite for
any non-trivial group G which is the fundamental group of a
spin spherical space form of dimension n=3 or
5.},
Key = {fds354056}
}

@article{fds354058,
Author = {D.Kazaras, C. Sormani and students David Afrifa and Victoria
Antonetti, Moshe Dinowitz and Hindy Drillick and Maziar Farahzad and Shanell George and Aleah Lydeatte Hepburn and Leslie Trang Huynh and Emilio Minichiello and Julinda Mujo Pillati and Srivishnupreeth
Rendla, Ajmain Yamin},
Title = {Smocked metric spaces and their tangent cones},
Year = {2020},
Abstract = {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 and prove these tangent cones at infinity exist, are
unique, and are normed spaces. We close with a variety of
students, and doctoral students.},
Key = {fds354058}
}

@article{fds354060,
Author = {Sven Hirsch and Demetre Kazaras and Marcus Khuri},
Title = {Spacetime Harmonic Functions and the Mass of 3-Dimensional
Asymptotically Flat Initial Data for the Einstein
Equations},
Journal = {Journal of Differential Geometry},
Year = {2020},
Abstract = {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 terms of linear growth
spacetime harmonic functions' in addition to the
energy-momentum density of matter fields, and is valid
regardless of whether the dominant energy condition holds or
whether the data possess a boundary. A corollary of this
result is a new proof of the spacetime positive mass theorem
for complete initial data or those with weakly trapped
surface boundary, and includes the rigidity statement which
asserts that the mass vanishes if and only if the data arise
from Minkowski space. The proof has some analogy with both
the Witten spinorial approach as well as the marginally
outer trapped surface (MOTS) method of Eichmair, Huang, Lee,
and Schoen. Furthermore, this paper generalizes the harmonic
level set technique used in the Riemannian case by Bray,
Stern, and the second and third authors, albeit with a
different class of level sets. Thus, even in the
time-symmetric (Riemannian) case a new inequality is
achieved.},
Key = {fds354060}
}

%% Papers Submitted
@article{fds354057,
Author = {Demetre Kazaras},
Title = {Desingularizing positive scalar curvature
4-manifolds},
Year = {2020},
Abstract = {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}hler ALE surfaces discovered by
Lock-Viaclovsky. Next, we study psc 4-manifolds with metric
singularities along points and embedded circles. Our psc
null-bordisms are essential tools in a desingularization
process developed by Li-Mantoulidis. This allows us to prove
a non-existence result for singular psc metrics on
enlargeable 4-manifolds with uniformly Euclidean geometry.
As a consequence, we obtain a positive mass theorem for
asymptotically flat 4-manifolds with non-negative scalar
curvature and low regularity.},
Key = {fds354057}
}

@article{fds354059,
Author = {Hubert L. Bray and Demetre P. Kazaras and Marcus A. Khuri and Daniel
L. Stern},
Title = {Harmonic Functions and The Mass of 3-Dimensional
Asymptotically Flat Riemannian Manifolds},
Year = {2020},
Abstract = {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 positive mass theorem is
achieved in dimension three. The proof has parallels with
both the Schoen-Yau minimal hypersurface technique and
Witten's spinorial approach. In particular, the role of
harmonic spinors and the Lichnerowicz formula in Witten's
argument is replaced by that of harmonic functions and a
formula introduced by the fourth named author in recent
work, while the level sets of harmonic functions take on a
role similar to that of the Schoen-Yau minimal
hypersurfaces.},
Key = {fds354059}
}

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