Riemannian Geometry During the Second Half of the Twentieth Century

By M. Berger. 2000

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Laplace-Beltrami spectra as 'Shape-DNA' of surfaces and solids (2006, background): “Let f be a real-valued function, with f2C 2 , defined on a Riemannian manifold M (differentiable manifold with Riemannian metric, cf. Berger [7]).”
Kähler parabolicity and the Euler number of compact manifolds of non-positive sectional curvature (2001, background): “Added in proof: This paper was widely circulated in preprint form in the Fall of 1997 (cf. [ Be ], p 138).”
The sphere theorems for manifolds with positive scalar curvature (2011, background): “On the other hand, some important work on sphere theorems for manifolds with positive Ricci curvature have been made by several geometers (see [3, 14, 21, 30, 36, 39], etc.”
Curvature, connected sums, and Seiberg-Witten theory (2001, background): “Given a smooth compact n-dimensional manifold M , the canonical metric problem [6] would ask us to geometrize M by somehow endowing it with a preferred Riemannian metric.”
Geometric, topological and differentiable rigidity of submanifolds in space forms (2011, background): “During the past sixty years, there are many progresses on sphere theorems for Riemannian manifolds and submanifolds [2, 5, 8, 12, 13, 19].”