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Bibliography
Some research papers (PDF files)
(2008) Optimal transport and Perelman's reduced volume
, preprint
(2007) Dimensional reduction and the long-time behavior of
Ricci flow, preprint
(2006) Notes on Perelman's papers, with Bruce Kleiner, preprint
(2004) Ricci curvature for metric-measure spaces via optimal transport, with Cedric Villani, to appear, Annals of Math.
(2008) Some geometric calculations on Wasserstein space,
Comm. Math. Phys. 277, p. 423-437
(2007) Optimal transport and Ricci curvature for metric-measure spaces,
in Surveys in Differential Geometry, vol. XI, Metric and
Comparison Geometry, eds. J. Cheeger and K. Grove, International
Press, Somerville, MA, p. 229-257
(2007) Hamilton-Jacobi semigroup on length spaces and applications, with
Cedric Villani, Journal de Math. Pures et Appliquees 88, p. 219-229
(2007) On the long-time behavior of type-III Ricci flow solutions,
Math. Annalen 339, p. 627-666
(2007) The work of Grigory Perelman, Proc. of the
ICM 2006,
European Math. Soc. Publishing House,
Vol. I, p. 66-77
(2007) Remark about scalar curvature and Riemannian submersions,
Proc. of the AMS 135, p. 3375-3381
(2007) Weak curvature conditions and functional inequalities, with Cedric Villani, J. of Functional Analysis 245, p. 311-333
(2006) Local index theory over foliation groupoids, with Alexander Gorokhovsky, Advances in Mathematics 204, p. 413-447
(2005) Limit sets as examples in noncommutative geometry, K-Theory 34, p. 283-326
(2003) Remark about the spectrum of the p-form Laplacian under
a collapse with curvature bounded below, Proc. of the AMS 132,
p. 911-918
(2003) Some geometric properties of the Bakry-Emery-Ricci tensor,
Comm. Math. Helv. 78, p. 865-883
(2003) Local index theory over etale groupoids, with Alexander
Gorokhovsky, J. Reine Angew.
Math. (Crelle's Journal) 560, p. 151-198
(2003) Manifolds with quadratic curvature decay and fast volume
growth,
Math. Ann. 325, p. 525-541
(2002) Higher-degree analogs of the determinant line bundle,
Comm. Math. Phys. 230, p. 41-69
(2002) Collapsing and the differential form Laplacian : the case of
a smooth limit space, Duke Math. Journal 114, p. 267-306
(2002) Collapsing and Dirac-type operators,
Geom. Ded. 91, p. 175-196 (special issue on Partial Differential Equations
and their Applications to Geometry and Physics)
(2001) On the spectrum of a finite-volume negatively-curved manifold,
Amer. J. of Math. 123, p. 185-205
(2001) The Dirac operator and conformal compactification,
Internat. Math. Res. Notices 2001, No. 4, p. 171-178
(2000) On the homotopy invariance of higher signatures for manifolds
with boundary, with Eric Leichtnam and Paolo Piazza,
J. of Diff. Geom. 54, p. 561-633
(2000) Invariant currents on limit sets, Comm. Math. Helv. 75, p. 319-350
(2000) Manifolds with quadratic curvature decay and slow volume growth,
with Zhongmin Shen, Ann. Scient. de l'Ec. Norm. Sup. (4) 33, p. 275-290
(2000) Signatures and higher signatures of $S^1$-quotients,
Math. Annalen 316, p. 617-657
(2000) Delocalized $L^2$-invariants, J. Funct. Anal. 169, p. 1-31,
Erratum
(2000) Secondary analytic indices, in Regulators in
Analysis, Geometry and Number Theory, Birkhauser Prog. in Math. Series,
vol. 171, eds. A. Reznikov and N. Schappacher, Birkhauser, Boston,
p. 231-293
(2000) A-hat genus and collapsing, J. of Geom. Anal. 10, p. 529-543
(1999) Diffeomorphisms and noncommutative analytic torsion,
Mem. Amer. Math. Soc. 141, no. 673, viii + 56 pp.
(1999) Deficiencies of lattice subgroups of Lie groups, Bull. London Math.
Soc. 31, p. 191-195
(1999) Remark about heat diffusion on periodic spaces,
Proc. Amer. Math. Soc. 127, p. 1243-1249
(1998) Eta and torsion, in Symetries Quantiques (Les Houches 1995),
p. 947-955
(1997) Torus bundles and the group cohomology of GL(N,Z), with J.-M.
Bismut, J. Diff. Geom. 47, p. 196-236
(1997) $L^2$ cohomology of geometrically infinite hyperbolic 3-manifolds,
Geom. and Funct. Anal. 7, p. 81-119
(1996) The zero-in-the-spectrum question, Enseign. Math. 42, p. 341-376
(1995) $L^2$ topological invariants of 3-manifolds, with Wolfgang Lueck,
Inv. Math. 120, p. 15-60
(1995) Flat vector bundles, direct images and higher real analytic torsion,
with J.-M. Bismut, J. Amer. Math. Soc. 8, p. 291-363
(1994) Equivariant analytic torsion for group actions, J. Funct. Anal. 125,
p. 438-451
(1994) R/Z index theory, Comm. Anal. Geom. 2, p. 279-311
(1992) Superconnections and higher index theory, Geom. and Funct. Anal.
2, p. 421-454
(1990) Particle models and noncommutative geometry, with Alain Connes,
Nucl. Phys. B Proc. Suppl. 18B, p. 29-47
(1990) Torsion constraints in supergeometry, Comm. Math. Phys.
133, p. 563-615
(1988) Real anomalies, J. Math. Phys.
29, p. 1455-1464
(1986) Supersymmetric path integrals, Comm. Math. Phys.
108, p. 605-629
(1986) Renormalization group flow for general sigma models, Comm. Math. Phys. 107, p. 165-176
(1986) Bosonization in curved spacetime, Phys. Lett. B
173, p. 319-320
(1986) Eigenvalue bounds for the Dirac operator, Pac. J. Math.
125, p. 117-126
(1985) Degrees of freedom and quantization of anomalous gauge theories,
with Doug Rajaraman, Phys. Lett. B 165, p. 321-326
(1985) Effective actions and large-N limits, Comm. Math. Phys.
100, p. 133-140
(1984) The eta-function and some new anomalies, Phys. Lett. B
145, p. 179-180
(1984) The Yang-Mills collective-coordinate potential, Comm. Math. Phys.
95, p. 289-300
(1984) Vacuum charge and the eta function, Comm. Math. Phys.
93, p. 533-558
Other
(2002) Collapsing and the differential form Laplacian : the case of
a singular limit space
(2001) The geometry of supergravity torsion constraints, prepared for the 2001 Park City Mathematics Institute