Papers

Published Papers by Professor Sormani 

See also google scholar and mathscinet.  Survey articles, chapters, conference proceedings, and undergraduate research are on my surveys page.  For my most recent work see my preprints page. 

Published Research Articles:  

Past Five Years (2019-2024):

Brian Allen, Raquel Perales, and Christina Sormani, ``Volume Above Distance Below'' to appear in Journal of Differential Geometry (DMS1612049) (IAS)  (arxiv)

Christina Sormani, Wenchuan Tian, and Changliang Wang, ``An extreme limit with nonnegative scalar curvature" Nonlinear Analysis 239 (2024), 24 pp.  (NSF DMS1006059) (PSC CUNY) (reprint) (arxiv)

A Sakovich and C Sormani "The null distance encodes causality," Journal of Mathematical Physics Vol.64, Issue 1 (Jan 2023) (NSF DMS1612049) (PSCCUNY) (arxiv) (reprint)

M Graf and C Sormani, “Lorentzian area and volume estimates for integral mean curvature bounds,”  Developments in Lorentzian Geometry, Springer Proc. Math. Stat., 389 Springer, Cham, 2022, 105–128. (NSF DMS1612049) (arxiv)

J Basilio and C Sormani  "Sequences of three dimensional manifolds with positive scalar curvature" Differential Geometry and its Applications, Vol. 77, (2021)  (NSF DMS 1612049)  (arxiv)

B Allen and C Sormani “Relating Notions of Convergence in Geometric Analysis"  Nonlinear Analysis Vol 200 Nov 2020 (NSF DMS 1612049)  (arxiv) 

E Bryden, M Khuri, and C Sormani “Stability of the Spacetime Positive Mass Theorem in Spherical Symmetry” Journal of Geometric Analysis Vol 31 Issue 4 (2020) 4191-4239 (reprint) (arxiv preprint) (NSF DMS1612049)(SCGP)

J Basilio, D Kazaras, and C Sormani ``An intrinsic flat limit of Riemannian manifolds with no geodesics" Geometriae Dedicata Vol 204, 265-284 (2020) (arxiv) (online first) 21 pages (NSF DMS1612049 and Basilio DMS1006059)

B Allen and C Sormani “Contrasting Various Notions of Convergence in Geometric Analysis”  Pacific Journal of Mathematics Vol 303 (2019), No. 1, 1–46 (Figures by Penelope Chang) (arxiv preprint) (reprint) (NSF DMS 1612049) 

C Sormani and I Stavrov``Geometrostatic manifolds of small ADM Mass"   Communications on Pure and Applied Mathematics  Vol 72, Issue 6 June 2019, pp 1243-1287 (arxiv preprint)  (reprint)   (NSF DMS1309360)

Previous Five Years (2014-2018):

J Basilio, J Dodziuk, and C Sormani, ``Sewing Riemannian Manifolds with Positive Scalar Curvature" Journal of Geometric Analysis  December 2018, Volume 28, Issue 4, pp 3553–3602 (arxiv preprint)  (reprint)  (NSF DMS 1006059)

C Sormani,"Intrinsic Flat Arzela-Ascoli Theorems"  Communications in Analysis and Geometry Vol 26 No 6 (2018) 1317-1373 (citations) (reprint) (arxiv preprint)  (NSF DMS 1309360)

J Portegies and C Sormani, "Properties of the Intrinsic Flat Distance"   (arxiv preprint) (citations)(reprint) solicited for the Volume in Honor of Yuri Burago, editted by D Burago and S Buyalo,  Algebra i Analiz Issue 3, Volume 29 (2017)70-143. (NSF DMS 1006059)

A Sakovich and C Sormani, "Almost Rigidity of the Positive Mass Theorem for Asymptotically Hyperbolic Manifolds with Spherical Symmetry" an Editor's Choice in General Relativity and Gravitation,September (2017) 49:125. (NSF DMS 1612049) (arxiv preprint) (reprint) (citations) 

L-H Huang, D A Lee and C. Sormani, "Intrinsic flat stability of the Positive Mass Theorem for graphical hypersurfaces in Euclidean space" Journal fur die Riene und Angewandte Mathematik, Crelle's Journal, Vol. 727 (2017), 269-299.    (arxiv preprint)  (reprint) (citations) (NSF DMS 1309360)

C-Y Lin and C Sormani, "Bartnik's Mass and Hamilton's Modified Ricci Flow"  Annales Henri Poincare October 2016, Volume 17, Issue 10, pp 2783–2800 (reprint) (erratum with fix) (arxiv preprint inc fix) (citations) (NSF DMS 1309360)

Z Sinaei and C Sormani, "Intrinsic Flat Convergence of Covering Spaces"  Geometriae Dedicata, Vol 184 (2016) pages 83–114  (arxiv preprint) (reprint) (NSF DMS 1006059)

C Sormani and C Vega, "Null distance on a spacetime"  Classical and Quantum Gravity, 33 (2016) no 8 29 pages (arxiv preprint) (reprint) (NSF DMS 1309360)

C. Sormani and G. Wei, "Various Covering Spectra on Complete Metric Spaces"  solicited for Asian Journal of Mathematics Vol. 19, No 1, January 2015, pp 171-202.  (arxiv preprint) (reprint)

P. LeFloch and C. Sormani, "The Nonlinear Stability of Spaces with Low Regularity"  Journal of Functional Analysis, 268 (2015) no. 7 2005-2065.  (arxiv preprint) (reprint) (citations) (NSF DMS 1309360)

D. Lee and C. Sormani, "Stability of the Positive Mass Theorem for Rotationally Symmetric Riemannian Manifolds"  Journal fur die Riene und Angewandte Mathematik (Crelle's Journal), Vol 686 (January 2014) 187-220.  (arxiv preprint) (reprint) (citations)

R. Perales and C. Sormani, "Sequences of Open Riemannian Manifolds with Boundary"  Pacific Journal of Mathematics, 270 (2014), no. 2, pp. 423-471.  (arxiv preprint) (reprint) (citations) 

Previous Five Years (2009-2013):

C. Sormani, "The Tetrahedral Property and a new Gromov-Hausdorff Compactness Theorem"  Comptes Rendus Volume 351, Issues 3-4, February (2013), pp 119-122.  (arxiv preprint) (reprint)

S. Lakzian and C. Sormani, "Smooth Convergence away from Singular Sets"  Communications in Analysis and Geometry. Volume 21, Number 1, (2013) pp 39-104. (Figures by Penelope Chang) (arxiv preprint) (reprint) (citations) (errors are corrected on the arxiv preprint in 2020 and published in an erratum)

D. Lee and C. Sormani, "Near-equality in the Penrose Inequality for Rotationally Symmetric Riemannian Manifolds" Annales Henri Poincare November (2012), Volume 13, Issue 7, pp 1537-1556. (arxiv preprint) (reprint) (citations)

C. Sormani and S. Wenger, "The Intrinsic Flat Distance between Riemannian Manifolds and Integral Current Spaces"  Journal of Differential Geometry, Vol. 87 (2011) 117-199. (arxiv preprint) (reprint) (citations)

C Sormani and S Wenger, w/ Appendix by R. Schul and S Wenger, "Weak Convergence of Currents and Cancellation"  Calc. Var. P.D.E., Vol. 38, No 1-2, May, 2010 183-206. (arxiv preprint) (reprint) (citations)

C. Sormani and G. Wei,"The Cut-Off Covering Spectrum"  Transactions of the American Mathematical Society 362 (2010), 2339-2391.  (arxiv preprint)

K. Shankar and C. Sormani ,"Conjugate Points in Length Spaces"  Advances in Mathematics 220 (2009), pp. 791-830. (arxiv preprint Sept 2007, Nov 2007, Sept 2008) (reprint)

Six Years with Small Children (2003-2008):

See Papers and Children.

C. Sormani, "Convergence and the Length Spectrum"  Advances in Mathematics, Volume 213, Issue 1, 1 August 2007, Pages 405-439. ( arxiv preprint Feb 2006) (reprint)

C. Sormani and Guofang Wei, "The Covering Spectrum of a Compact Length Space"  Journal of Differential Geometry, Vol 67 (2004) 35-77.  (Arxiv posting Nov 2003) (reprint) [An Erratum in JDG 74 (2006) 523-3: Example 10.3 is not correct. All else OK.] 

C. Sormani, "Friedmann Cosmology and Almost Isotropy"   Geometric and Functional Analysis, Vol. 14 (2004) 853-912. (Arxiv posting Feb 2003, Mar 2004) (reprint)

C. Sormani and Guofang Wei, "Universal Covers for Hausdorff Limits of Noncompact Spaces"  Transactions of the American Mathematical Society 356 (2004), no. 3 pp. 1233-1270. (Arxiv ) (reprint)

First Five Years (1998-2002):

C. Sormani and Guofang Wei,"Hausdorff Convergence and Universal Covers"  Transactions of the American Mathematical Society 353 (2001), no. 9, 3585--3602. pdf copy (preprint Aug 2000) (reprint)

Zhongmin Shen and Christina Sormani. "The Codimension One Homology of a Complete Manifold with Nonnegative Ricci Curvature"   American Journal of Mathematics 123 (2001), no. 3, 515--524. (reprint)  (preprint Sep 1999, Nov 2000)

C Sormani, "On Loops Representing Elements of the Fundamental Group of a Complete Manifold with Nonnegative Ricci Curvature"   Indiana Journal of Mathematics, 50 (2001) no. 4, 1867-1883. (reprint) (preprint April 1999)

C Sormani, "Nonnegative Ricci Curvature, Small Linear Diameter Growth, and Finite Generation of Fundamental Groups"   Journal of Differential Geometry 54 (2000), no. 3, 547--559 (reprint.pdf)  (preprint Sept 1998)

C Sormani, "Harmonic Functions on Manifolds with Nonnegative Ricci Curvature and Linear Volume Growth"  Pacific Journal of Mathematics.Vol 192, No 1, 183-189, January 2000. (preprint March 1999) (reprint)

C Sormani, "The Rigidity and Almost Rigidity of Manifolds with Lower Bounds on Ricci Curvature and Minimal Volume Growth" Communications in Analysis and Geometry. Vol 8, No. 1, 159-212, January 2000.  (preprint May 1996, March 1999) (reprint)

C Sormani, "Busemann Functions on Manifolds with Lower Ricci Curvature Bounds and Minimal Volume Growth" Journal of Differential Geometry 48, (1998) 557-585. (reprint) (preprint May 1996, Nov 1997) (see also my doctoral dissertation) 

Note that most papers in mathematics are published 1-3 years after being posted on the arxiv: especially longer papers with significant material for the referees to check.

For my latest work, go to my preprints webpage. 

Old Homepage: http://comet.lehman.cuny.edu/sormani    Moved to: https://sites.google.com/site/professorsormani/