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Christina Sormani's Papers

Preprints:

"Conjugate Points in Length Spaces"
by Krishnan Shankar and Christina Sormani
Complete v2 preprint on the arxiv and submitted (Sept 2007, Nov 2007),
"The Cut-Off Covering Spectrum"
by Christina Sormani and Guofang Wei,
complete preprint on arxiv and submitted (May 2007)
"Various Covering Spectra for Complete Spaces"
by Christina Sormani and Guofang Wei,
preliminary preprint regarding Shift and Rescaled Covering Spectra is available upon request,
we are awaiting the appearance of announced preprint before finalizing this paper

Published Research Articles:

"Busemann Functions on Manifolds with Lower Ricci Curvature
Bounds and Minimal Volume Growth",
by Christina Sormani
Journal of Differential Geometry 48, (1998) 557-585.
Email me for a copy or view the abstract. (May 1996, Nov 1997)

"The Rigidity and Almost Rigidity of Manifolds with Lower Bounds on
Ricci Curvature and Minimal Volume Growth",
by Christina Sormani
Communications in Analysis and Geometry. Vol 8, No. 1, 159-212, January 2000.
Download a copy or view the abstract. (May 1996, March 1999)
"Harmonic Functions on Manifolds with Nonnegative Ricci Curvature
and Linear Volume Growth"
by Christina Sormani
Pacific Journal of Mathematics.Vol 192, No 1, 183-189, January 2000.
Download a copy or view the abstract. (March 1999)
"Nonnegative Ricci Curvature, Small Linear Diameter Growth, and
Finite Generation of Fundamental Groups"
by Christina Sormani.
Journal of Differential Geometry 54 (2000), no. 3, 547--559 reprint.pdf.
Download a copy or view the abstract (Sept 1998)
"On Loops Representing Elements of the Fundamental Group of a
Complete Manifold with Nonnegative Ricci Curvature"
by Christina Sormani.
Indiana Journal of Mathematics, 50 (2001) no. 4, 1867-1883. reprint
Download a copy or view the abstract (April 1999)
"The Codimension One Homology of a Complete Manifold with
Nonnegative Ricci Curvature"
by Zhongmin Shen and Christina Sormani.
American Journal of Mathematics 123 (2001), no. 3, 515--524. reprint
Download a postscript copy or view the abstract. (Sep 1999, Nov 2000)
"Hausdorff Convergence and Universal Covers"
by Christina Sormani and Guofang Wei
Transactions of the American Mathematical Society 353 (2001), no. 9, 3585--3602. reprint
Download a postscript copy , pdf copy , or view the abstract. (Aug 2000)
"Universal Covers for Hausdorff Limits of Noncompact Spaces"
by Christina Sormani and Guofang Wei
Transactions of the American Mathematical Society 356 (2004), no. 3 pp. 1233-1270. reprint.
Arxiv preprint (July 2002)
"Friedmann Cosmology and Almost Isotropy"
by Christina Sormani
GAFA, Geom. funct. anal. Vol. 14 (2004) 853-912. reprint
A physics proceedings paper announcing these results is here and will appear in the conference proceedings.
Arxiv posting (Feb 2003, Mar 2004)
"The Covering Spectrum of a Compact Length Space"
by Christina Sormani and Guofang Wei
Journal of Differential Geometry, Vol 67 (2004) 35-77. reprint.pdf.
An Erratum in JDG 74 (2006) 523-3: Example 10.3 is not correct. All else OK.
Arxiv posting, (Nov 2003)
"Convergence and the Length Spectrum"
by Christina Sormani, recommended for graduate students, has an open problem list, 30 pages,
Advances in Mathematics, Volume 213, Issue 1, 1 August 2007, Pages 405-439. reprint.
preprint.pdf (Feb 2006)

Survey Articles:

"The Topology of Open Manifolds of Nonnegative Ricci Curvature"
by Zhongmin Shen and Christina Sormani
Midwest Geometry Conference Proceedings 2006, JGPAM, January 2008 (solicited and refereed).
A survey article, 31 pages, many diagrams and open problems preprintnov2006.pdf, (June 2006, Nov 2006)