University of Illinois at Urbana-Champaign

Recent Publications by 
Stephanie Alexander
Department of Mathematics

(with M. Ghomi and J. Wong), Topology of nonnegatively curved hypersurfaces spanning a prescribed boundary in $R^n$ (pdf), submitted.

(with R. Bishop and R. Ghrist), Capture pursuit games on unbounded domains with boundary (pdf), submitted.

(with V. Kapovitch and A. Petrunin), An optimal lower curvature bound for convex hypersurfaces in Riemannian manifolds (pdf), Illinois J. Math., to appear.

(with R.L. Bishop), Lorentz and semi-Riemannian spaces with Alexandrov curvature bounds, Comm. Anal. Geom. 16 (2008), 251-282. (pdf), ( ps ), .

(with R. Bishop and R. Ghrist), Pursuit and evasion in non-convex domains of arbitrary dimension (pdf), Proc. Robotics Systems & Science (2006).

(with R. L. Bishop), Gauss equation and injectivity radii for subspaces in spaces of curvature bounded above, (pdf), ( ps ), Geometriae Dedicata 117 (2006), 65-84.

_____, A cone splitting theorem for Alexandrov spaces, (pdf), (ps), Pacific J. Math. 218 (2005), 1-16.

_____, Curvature bounds for warped products of metric spaces (pdf), (ps), Geom.Funct. Anal. 14 (2004) 1143-1181.

(with M. Ghomi), The convex hull property of noncompact hypersurfaces with positive curvature (pdf), Amer. J. Math. 126 (2004) 891-897.

(with R. L. Bishop), Spines and topology of thin Riemannian manifolds with boundary (pdf), (ps), Trans. A.M.S. 355 (2003) 4933-4954.

(with M. Ghomi), The convex hull property and topology of hypersurfaces with nonnegative curvature, Advances in Math. 180 (2003) 324-354.

(with R. L. Bishop), FK-convex functions on metric spaces, Manuscripta Math. 110 (2003) 115-133.

_____, Spines and homology of thin Riemannian manifolds with boundary, Advances in Math. 155 (2000) 23-48.

______, Warped products of Hadamard spaces, Manuscripta Math. 96 (1998) 487-505.

 ______, The Fary-Milnor theorem in Hadamard manifolds, Proc. Amer. Math. Soc. 126 (1998) 3427-3436.

 ______, Thin Riemannian manifolds with boundary, Math. Annalen 310 (1998) 601-616

 ______, Racetracks and extremal problems for curves of bounded curvature in metric spaces, Geometriae Dedicata 66 (1997) 331-341.

 ______, Comparison theorems for curves of bounded geodesic curvature in metric spaces of curvature bounded above, Diff. Geom. App. 6 (1996) 67- 86.

 (with I.D. Berg, R.L. Bishop) Cut loci, minimizers and wave fronts in Riemannian manifolds with boundary}, Michigan Math. J. 40 (1993) 229-237.

 (with R. J. Currier) Hypersurfaces and nonnegative curvature, Differential Geometry (R. E. Greene, S.-T. Yau, eds.), Proc. Symposia in Pure Math. 54 (part 3) (1993) 37-44.

 (with I. D. Berg, R. L. Bishop) The distance geometry of Riemannian manifolds with boundary, Differential Geometry (R. E. Greene, S.-T. Yau, eds.), Proc. Symposia in Pure Math. 54 (part 3) (1993), 31-36.

 ______, Geometric curvature bounds in Riemannian manifolds with boundary, Trans. Amer. Math. Soc. 339 (1993) 703-716.

 (with R.J. Currier) Nonnegatively curved ends of Euclidean hypersurfaces, Geom. Dedicata 40 (1991) 29-43.

 (with R.L. Bishop) The Hadamard-Cartan theorem in locally convex metric spaces, Enseign. Math. 36 (1990) 309-320.

 (with R.J. Currier) Nonnegatively curved hypersurfaces of hyperbolic space and subharmonic functions, J. London Math. Soc. (2) 41 (1990) 347-360.

Last updated aug07