%% 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 = {265284},
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 msphere 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 = {12},
Pages = {189224},
Year = {2018},
Abstract = {Let (Y, g) be a compact Riemannian manifold of positive
scalar curvature (psc). It is wellknown, due to
Schoen–Yau, that any closed stable minimal hypersurface of
Y also admits a pscmetric. 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
pscbordism. For instance, assume (Y_0,g_0) and (Y_1,g_1)
are closed pscmanifolds equipped with stable minimal
hypersurfaces X_0 \subset Y_0 and X_1\subset Y_1. Under
natural topological conditions, we show that a pscbordism
(Z,{\bar{g}}) : (Y_0,g_0)\rightsquigarrow (Y_1,g_1) gives
rise to a pscbordism between X_0 and X_1 equipped with the
pscmetrics 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 scalarflat 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
SchoenYau 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 = {361372},
Year = {2012},
Month = {Summer},
ISSN = {00308730},
Abstract = {We give an explicit formula for all curves of constant
torsion in the unit twosphere. 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 endperiodic manifolds},
Journal = {Communications in Analysis and Geometry},
Volume = {to appear, accepted 2019},
Year = {2020},
Abstract = {We show that the periodic ηinvariants introduced by
MrowkaRubermanSaveliev~\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 SchoenYau
minimal surface technique with an endperiodic 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 nontrivial 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 GromovHausdorff
limits and prove these tangent cones at infinity exist, are
unique, and are normed spaces. We close with a variety of
open questions suitable for advanced undergraduates, masters
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 3Dimensional
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
energymomentum vector (ADM mass) of 3dimensional
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
energymomentum 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
timesymmetric (Riemannian) case a new inequality is
achieved.},
Key = {fds354060}
}
%% Papers Submitted
@article{fds354057,
Author = {Demetre Kazaras},
Title = {Desingularizing positive scalar curvature
4manifolds},
Year = {2020},
Abstract = {We show that the bordism group of closed 3manifolds with
positive scalar curvature (psc) metrics is trivial by
explicit methods. Our constructions are derived from
scalarflat K{ä}hler ALE surfaces discovered by
LockViaclovsky. Next, we study psc 4manifolds with metric
singularities along points and embedded circles. Our psc
nullbordisms are essential tools in a desingularization
process developed by LiMantoulidis. This allows us to prove
a nonexistence result for singular psc metrics on
enlargeable 4manifolds with uniformly Euclidean geometry.
As a consequence, we obtain a positive mass theorem for
asymptotically flat 4manifolds with nonnegative 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 3Dimensional
Asymptotically Flat Riemannian Manifolds},
Year = {2020},
Abstract = {An explicit lower bound for the mass of an asymptotically
flat Riemannian 3manifold 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 SchoenYau 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 SchoenYau minimal
hypersurfaces.},
Key = {fds354059}
}
