Vitali Kapovitch's Home Page
Department of Mathematics,
University of Toronto,
Toronto, Ontario, Canada M5S 2E4
Office:
45 St George st (PGB), room 201c
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:
Research
Interests:
I'm interested in global
Riemannian geometry. More specifically,
I'm interested in convergence with lower
sectional and Ricci curvature bounds.
My book with Anton Petrunin and
Stephanie Alexander "Invitation
to Alexandrov geometry:
CAT(0) spaces" has been published
by Springer.
Publications/Preprints
(which
can also be downloaded here)
- Alexandrov
geometry: foundations, vol
1, with S. Alexander and A.
Petrunin, 2022.
- Remarks
on manifolds with two sided
curvature bounds, with
A. Lytchak,
2021, to
appear in
Analysis and
Geometry in
Metric Spaces.
- Structure
of submetries, with A.
Lytchak, 2020, to appear in
G&T.
- On
gluing Alexandrov spaces with
lower Ricci curvature bounds,
with C. Ketterer and K.-T.
Sturm, 2020.
- Mixed
curvature almost flat
manifolds, 2019,
accepted for publication in
Geometry & Topology
- On
the structure of RCD spaces
with upper curvature bounds,
with
M. Kell and C. Ketterer, 2019
- On the
topology and the boundary of
N-dimensional RCD(K,N) spaces,
with A. Mondino, Geometry &
Topology 25, (2021), 445–495
- Weakly
non-collapsed RCD spaces with
upper curvature bounds,
with
C. Ketterer,
Analysis and
Geometry in
Metric
Spaces,
7 (2019), no.
1, 197–211
- On
Torsion in the Center
Conjecture, (with
A. Petrunin
and W.
Tuschmann),
Electron. Res.
Announc. Math.
Sci. 25
(2018), 27–35.
- CD meets
CAT, with C.
Ketterer, J.
Reine Angew.
Math.
(Crelles Journal), 0.0 (2019), doi:10.1515/crelle-2019-0021.
- Metric-measure
boundary and geodesic
flow on Alexandrov
spaces, with A.
Lytchak and A. Petrunin, 2017,
accepted for publication in JEMS.
- Invitation
to Alexandrov geometry,
(with
S. Alexander
and A.
Petrunin),
Springer
Briefs, 2019.
- On
noncollapsed almost Ricci-flat
4-manifolds, (with John
Lott), Amer. J. Math. 141
(2019), no. 3, 737--755.
- On
dimensions of tangent cones in
limit spaces with lower Ricci
curvature bounds, (with Nan
Li),
J. Reine Angew. Math. (Crelles
Journal), 742
(2018), 263–280.
- Space
of nonnegatively curved metrics
and pseudoisotopies, (with
Igor Belegradek and Tom
Farrell), J. Differential
Geom. 105 (2017), no. 3,
345--374.
- 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