Department of Mathematics

(with V. Kapovitch & A. Petrunin), Alexandrov Geometry (book, 238 p.), http://arxiv.org/abs/1903.08539.

(with V .Kapovitch & A. Petrunin), Invitation to Alexandrov Geometry: CAT(0) Spaces (mini-book, 98 p.), SpringerBriefs in Mathematics, to appear. http://arxiv.org/abs/1701.03483

(with W. Karr), Space-time convex functions and sectional curvature, Lorentzian geometry and related topics, Springer Proc. Math. Stat., 211 (2017), 13-26. http://arxiv.org/abs/1702.02652

(with W. Karr), Convex functions and geodesic connectedness of space-times, Diff. Geom. App., 54PB (2017) pp. 361-384. http://arxiv.org/abs/1510.04228v2

(with R. Bishop), Warped products admitting a curvature bound, Advances in Math. 303 (2016) 88 - 122. http://arxiv.org/abs/1509.00380

(with V. Kapovitch and A. Petrunin), Alexandrov meets Kirszbraun (pdf), Proc. Gokova Geometry-Topology Conference 2010, S. Akbulut, D. Auroux, T. Onder, eds., International Press (2011), 88- 109.

(with M. Ghomi and J. Wong), Topology of nonnegatively curved hypersurfaces spanning a prescribed boundary in $R^n$ (pdf), Duke Math. J.152 (2010), 533-565.

(with R. Bishop and R. Ghrist), Total curvature and simple pursuit on domains of curvature bounded above (pdf), Geom. Dedicata 149 (2010), 275 - 290.

(with R. Bishop), Extrinsic curvature of semiconvex subspaces in Alexandrov geometry (pdf), Annals Global Anal. Geom. 37 (2010), 241-262.

(with R. Bishop and R. Ghrist), Capture pursuit games on unbounded domains with boundary (pdf), l'Enseignement Math. 55 (2009), 103-125.

(with V. Kapovitch and A. Petrunin), An optimal lower curvature bound for convex hypersurfaces in Riemannian manifolds (pdf), Illinois J. Math. 52 (2008), 1031-1033.

(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. (GAFA) 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 (pdf), 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 (pdf), 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 june2010*