Bruce Kleiner

Bruce Kleiner in Oberwolfach , 2004

Bruce Alan Kleiner is an American mathematician.

Life

Kleiner studied at the University of California, Berkeley (bachelor's degree 1985), where he received his doctorate in 1990 under Wu-Yi Hsiang (Riemannian Four-Manifolds with Nonnegative Curvature and Continuous Symmetry). He then taught at the University of Pennsylvania , the University of Utah (as Associate Professor 1998), the University of Michigan , Yale University . He is currently a professor at New York University .

Kleiner deals with differential geometry, including the Ricci River , an essential part of Grigori Perelman's proof of the Poincaré conjecture . With John Lott he was a member of one of three teams that confirmed Perelman's evidence, examined it in detail and filled in gaps. In addition, he deals with geometric analysis and geometric group theory. With Bernhard Leeb , he proved the assumption, which goes back to Margulis , that quasi-isometries between symmetrical spaces of rank after rescaling have a finite distance from an isometry. In 2007 he found a simplified proof of Gromow's theorem on groups of polynomial growth. With Jeff Cheeger he wrote fundamental work on analysis on metric spaces. ${\displaystyle \geq 2}$

Kleiner was Sloan Research Fellow , Clay Research Fellow and Invited Speaker at the ICM 2006 (The asymptotic geometry of negatively curved spaces: uniformization, geometrization and rigidity). In 2013 he and John Lott received the NAS Award for Scientific Reviewing .

Fonts

• (with Bernhard Leeb ) Rigidity of quasi-isometries for symmetric spaces and Euclidean buildings . In: Inst. Hautes Études Sci. Publ. Math. , No. 86, 1997, pp. 115-197.
• (with Mario Bonk ) Quasisymmetric parametrizations of two-dimensional metric spheres . In: Invent. Math. , 150, 2002, no. 1, pp. 127-183.
• (with John Lott ) Notes on Perelman's Papers , 2006. In: Geom. Topol. , 12, 2008, no. 5, pp. 2587-2855, arxiv : math / 0605667 .
• A new proof of Gromov's theorem on groups of polynomial growth , 2007. In: J. Amer. Math. Soc. , 23, 2010, no. 3, pp. 815-829, arxiv : 0710.4593 .
• (with Jeff Cheeger ) Differentiating maps into , and the geometry of BV functions ${\displaystyle L^{1}}$ . In: Ann. of Math. , (2) 171, 2010, no. 2, pp. 1347-1385.
• (John Lott): Singular Ricci flows I . In: Acta Math. , 219, 2017, no. 1, pp. 65-134.
• The asymptotic geometry of negatively curved spaces: uniformization, geometrization and rigidity (PDF; 142 kB) ICM 2006.

Web links

• Bruce Kleiner at New York University