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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
             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 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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