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Publications

Books
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1) "Perelman’s Entropy Functional and No Local Collapsing", ISBN of the book version: 978­3­8473­7250­9 (2011) Spring 2011
Conference Papers
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1) "A Priori Estimates and the Geometry of the Monge­ Ampère Equation (After Luis Caffarelli)", Proc. of Summer School on Optimal Transport and Applications, UCLA (2013) Summer 2013
2) "Geometric singularities under the Gigli-Mantegazza flow", Mean Curvature Flow Proceedings of the John H. Barrett Memorial Lectures held at the University of Tennessee, Knoxville, May 29–June 1, 2018 Winter 2020
PhD Thesis
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1) "Smooth Convergence Away From Singular Sets and Intrinsic Flat Continuity of Ricci Flow", PhD Thesis (2013) Spring 2013
Journal Papers
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1) "Smooth Convergence Away From Singularities", joint with C. Sormani, Communications in Analysis and Geometry 21, no. 1, 39–104 (2013) Winter 2013
2) "Metric perspectives of the Ricci flow applied to disjoint unions", joint with M. Munn, Analysis and Geometry in Metric Spaces 2, 282–293 (2014) Fall 2014
4) "Intrinsic flat continuity of Ricci Flow Through Neck Pinch Singularities", Geometriae Dedicata 179, 69–89 (2015) Spring 2015
3) "Differential Harnack estimates for heat equation under Finsler­ Ricci flow", Pacific Journal of Mathematics 278, no. 2, 447–462 (2015) Winter 2015
5) "Non­-branching RCD(0, N) geodesic spaces with Small linear diameter growth have finitely generated fundamental groups", joint with Y. Kitabeppu, Canadian Mathematical Bulletin 58, no. 4, 787­798 (2015) Spring 2015
6) "Characterization of low dimensional RCD*(K,N) spaces", joint with Y. Kitabeppu, Analysis and Geometry in Metric Spaces 4, 187 ­ 215 (2016) Summer 2016
7) "Diameter controls and smooth convergence away from singularities", Journal of Differential Geometry and its Applications 47, 99­129 (2016) Summer 2016
8) "Geometric singularities and a flow tangent to Ricci flow", joint with L. Bandara and M. Munn, Annali della Scuola Normale Superiore di Pisa, Classe di Scienze 17, no. 2, 763 ­ 804 (2017) Summer 2017
9) "A global Poincare inequality on graphs via a conical curvature­ dimension conditions", joint with Z. McGuirk, Analysis and Geometry in Metric Spaces (2018) Winter 2018
11) Errata to "Smooth convergence away from singular sets", Communications in Analysis and Geometry Volume 28, Number 7, 1755–1772, 2020 Fall 2020
10) "Bubble tree convergence for harmonic maps into compact locally CAT(1) spaces", joint with C. Breiner, Calculus of Variations and Partial Differential Equations volume 59, Article number: 144 (2020) Summer 2020
12) "On Weak Super Ricci Flow Through Neckpinch", joint with M. Munn, Analysis and Geometry in Metric Spaces, volume 9, pp 120 --159 (2021) Summer 2021
13) "Bakry-Emery Ricci curvature of doubly warped product of weighted spaces", joint with Z. Fathi, Journal of Geometric Analysis vol32, issue 79, 75pp (2022) Winter 2022
14) "The rigidity of sharp spectral gap in nonnegatively curved spaces", joint with C. Ketterer and Y. Kitabeppu, Nonlinear Analysis Vol 228 (2023) Winter 2023
Preprints
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1) "Discrete Ollivier-Ricci curvature", joint with Z. Fathi. Spring 2022
2) "On rigidity of ALE vector bundles", joint with F. Asadi and Z. Fathi Spring 2023

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