A Pinching Theorem for Homotopy Spheres

Karsten Grove, Peter Petersen

Type: Article

Publication Date: 1990-07-01

Citations: 15

DOI: https://doi.org/10.2307/1990933

Abstract

The (length) excess of a triangle measures how much the triangle inequality fails to be an equality.This notion was first studied seriously in [AG].We say that a (bounded) metric space X = (X, d) has excess :5 e if there are points p, q E X such that d(p, x)+d(x, q) ~ d(p, q)+e for all x EX.The excess, e(X) , of X is the infimum of all e ~ 0 where X has excess ~ e.

Locations

Journal of the American Mathematical Society - View - PDF

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Works That Cite This (16)

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+ PDF Chat	Curvature, triameter, and beyond	1992	Karsten Grove Steen Markvorsen
+ PDF Chat	New extremal problems for the Riemannian recognition program via Alexandrov geometry	1995	Karsten Grove Steen Markvorsen
+ PDF Chat	Exotic spheres and curvature	2008	M. Joachim David J. Wraith
+ PDF Chat	An excess sphere theorem	1993	Peter Petersen Shunhui Zhu
+ PDF Chat	Smooth diameter and eigenvalue rigidity in positive Ricci curvature	2001	Wilderich Tuschmann
+ PDF Chat	Stabilité de l'inégalité de Faber-Krahn en courbure de Ricci positive	2005	Jérôme Bertrand
+ PDF Chat	Manifolds of Positive Ricci Curvature with Almost Maximal Volume	1994	G. Perelman
+ PDF Chat	Manifolds near the boundary of existence	1991	Karsten Grove Peter Petersen
+ PDF Chat	Manifolds of positive Ricci curvature with almost maximal volume	1994	G. Perelman
+ PDF Chat	Pincement spectral en courbure de Ricci positive	2007	Jérôme Bertrand

Works Cited by This (14)

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+ PDF Chat	The topology of certain Riemannian manifolds with positive Ricci curvature	1983	Yoe Itokawa
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+ PDF Chat	A finiteness theorem for metric spaces	1990	V Peter Petersen
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+	Bounding Homotopy Types by Geometry	1988	Karsten Grove Peter Petersen
+	Curvature, diameter and betti numbers	1981	Michael Gromov
+	Geometric finiteness theorems via controlled topology	1990	Karsten Grove Peter Petersen Jyh-Yang Wu
+	Metrics of positive ricci curvature with large diameter	1990	Michael T. Anderson
+	On manifolds of positive Ricci curvature with large diameter	1991	Yukio Otsu