Vitali Kapovitch's Home Page
Department of Mathematics,
University of Toronto,
Toronto, Ontario, Canada M5S 2E4
Office:
ES 2146
Telephone: (416)-978-6786
Fax:
(416) 978-4107
E-mail:
vtk@math.toronto.edu
"God
put me on Earth to
accomplish a certain
number
of things. Right now I am so far behind I will never die."
--Bill
Watterson
Teaching:
- Fall 2008-Winter 2009: MAT257
- Fall 2007: MAT267
- Fall
2006: MAT247
- Winter 2007: MAT267
- Wolfgang Meyer's notes on
comparison geometry. On Tuesday, October 2 the comparison geometry
class will have an extra lecture from 12-1pm in BA 6290B.
Research
Interests: I'm interested in
global Riemannian geometry. More specifically, I'm interested in
convergence with lower sectional and Ricci curvature bounds and
manifolds of pinched negative curvature.
Workshop on Curvature and Global Shape.
Publications/Preprints
(which can
also be
downloaded
here)
- Perelman's Stability Theorem,
To
be published in Surveys in Comparison Geometry.
- Nilpotency,
almost
nonnegative curvature and the gradient push, (with
A.
Petrunin and W.
Tuschmann), 2005, to appear in Annals of Mathematics.
- Nonnegative pinching, moduli
spaces
and bundles with infinitely many souls,(with
A. Petrunin and W.
Tuschmann), Journal of Diff.
Geometry, 71, (2005), no. 3,
pp. 365-383.
- Pinching
estimates for
negatively curved manifolds with nilpotent fundamental groups,(with
I. Belegradek), Geom. Funct. Anal. 15, (2005), no. 5, 929--938.
- Curvature
bounds via
Ricci smoothing, Illinois Journal of
Mathematics, 49, (2005) no. 1, pp.259-263,
- (with
I. Belegradek) Classification of
negatively pinched
manifolds with amenable fundamental groups
, to appear in Acta Mathematica
- Biquotients
with
singly
generated
rational cohomology, (with W.
Ziller), Geometriae Dedicata,
104 (1):
149--160, 2004
- Restrictions
on
collapsing with
a lower sectional curvature bound,
Mathematische Zeitschrift, 249,
(2005),no.3, pp.
519 - 539
- A
note on
rational
homotopy
of biquotients, preprint
- Regularity
of
limits of
noncollapsing
sequences of manifolds, Geom.
Funct. Anal. 12
(2002), no.
1,
121--137.
- (with
I.Belegradek)
Obstructions
to nonnegative curvature and rational homotopy theory,
Journal of
AMS, 16
(2003), 259-284.
- (with
I.Belegradek)
Finiteness
theorems
for nonnegatively curved vector bundles, Duke
Mathematical
Journal, 108
(2001), no. 1, pp. 109--134.
- (with
I.Belegradek)
Topological
obstructions to nonnegative curvature,
Math. Ann. 320 (2001),
no. 1, 167--190.
- (with
L. Guijarro)
Restrictions on
the geometry at infinity of nonnegatively curved manifolds,
Duke
Math.
J. 78
(1995), no. 2, 257--276.
Here are some geometry links:
This
home page
is always under
construction 