# Page history

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## 13 January 2015

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## 5 April 2014

## 13 January 2014

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## 14 September 2012

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## 12 October 2011

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## 19 December 2009

## 7 September 2009

## 4 September 2009

CAT(0) →Metric geometry

+58

mention contractibility →Generalization to locally convex spaces

+71

→References: alink

+51

now the statement of the theorem is somewhat redundant. →Metric geometry

-276

ok. i was able to track down that Alexander and Bishop paper. Inserting their generalization here. →Theorem

+802

copyedit →Theorem

-69

I see no indication that Ballmann only proved this for locally compact spaces.

-31

→Riemannian geometry

m-1

ce

m-1

rm sentence about geodesic spaces. →Metric geometry

-89

Harvard references

+67

rm local compactness, as this never was essential to the Riemannian theorem anyway. →Metric geometry

m+37

+ →References

+493

not stronger, actually. →Riemannian geometry

m+24

Case of Hilbert manifolds (thus obviating the remark below about local compactness). →Riemannian geometry

+365

→Metric geometry

m+4

corrected: not many people would consider this the definition of a convex metric space. "Non-positively curved" is much more typical. →Metric geometry

+368

some edits for WP:NPOV: surely nothing is less "modern" about conventional Riemannian geometry, just because this theorem has been generalized to other areas.

major omission is surely the classical formulation. →Modern formulation

+435