Vitali Kapovitch's Home Page
Department of Mathematics,
University of Toronto,
Toronto, Ontario, Canada M5S 2E4
Office:
HU 1023
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
Anyone
who cannot cope with Mathematics is
not fully human. At best he is a
tolerable subhuman who has learned to
wear shoes, bathe, and not make messes
in the house.
Notebooks
of Lazarus Long, "Time
Enough for Love", by Robert
A. Heinlein
Teaching:
Research
Interests:
I'm interested in global
Riemannian geometry. More specifically,
I'm interested in convergence with lower
sectional and Ricci curvature bounds.
Here are the
notes from my lectures at SMS
2011
Summer
School
on
“Metric
Measure
Spaces:
Geometric
and
Analytic
Aspects”.
I'm currently working on a book on
spaces with curvature bounded below and
above together with Stephganie
Alexander and Anton Petrunin.
Here is a
section on definitions of Alexandrov
spaces and the proof of the
globalization theorem from this
book.
Workshop on
Curvature and Global Shape.
Publications/Preprints
(which
can also be downloaded here)
- Manifolds
without conjugate points and
their fundamental groups,
(with S. Ivanov),
J. Differential Geom.
96
(2014),
no. 2, 223–240.
- On
fibrations with formal elliptic
fibers, (with M. Amann),
Adv. Math.
231
(2012),
no. 3-4, 2048–2068.
- Structure
of fundamental groups of
manifolds with Ricci curvature
bounded below, (with B.
Wilking), 2011
- Alexandrov
meets Kirzbraun, (with
S. Alexander and A. Petrunin) ,
Proceedings of the 17th Gökova
Gemometry and Topology Conference,
2010
- An optimal
lower curvature bound for convex
hypersurfaces in Riemannian
manifolds, (with S.
Alexander, and A. Petrunin)
, Illinois Journal of Mathematics,
vol. 52, (2009), No 3, pp
1031-1033
- Perelman's
Stability Theorem,
Surveys in
Differential
geometry,
Metric and
Comparison
geometry, vol XI
,
International
press,
(2007),
103-136
- Nilpotency,
almost
nonnegative
curvature and the gradient push,
(with A.
Petrunin and W.
Tuschmann), Annals of
Mathematics, Vol. 171
(2010), No. 1, 343-373
- 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 , Acta Math. 196
(2006), no. 2, 229–260
- 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