Sphere theorem

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Sphere theorem

Quality:

Sphere theorem - theorem stating that a complete, simply-connected, n-dimensional Riemannian manifold with sectional curvature taking values in the interval (1, 4] is homeomorphic to the n-sphere. Article “Sphere theorem” in English Wikipedia has 15 points for quality (as of July 1, 2025). The article contains 5 references and 3 sections.

This article has the best quality in German Wikipedia. However, this article is the most popular in English version.

Since the creation of article “Sphere theorem”, its content was written by 24 registered users of English Wikipedia and edited by 65 registered Wikipedia users in all languages.

The article is cited 25 times in English Wikipedia and cited 65 times in all languages.

The highest Authors Interest rank from 2001:

  • Local (English): #213325 in February 2024
  • Global: #236810 in November 2010

The highest popularity rank from 2008:

  • Local (English): #835522 in September 2023
  • Global: #1328782 in September 2023

There are 5 language versions for this article in the WikiRank database (of the considered 55 Wikipedia language editions).

The quality and popularity assessment was based on Wikipédia dumps from July 1, 2025 (including revision history and pageviews for previous years).

The table below shows the language versions of the article with the highest quality.

Languages with the highest quality

#LanguageQuality gradeQuality score
1German (de)
Sphärensatz
31.575
2French (fr)
Théorème de la sphère
20.9374
3English (en)
Sphere theorem
14.9945
4Russian (ru)
Теорема о сфере (дифференциальная геометрия)
7.248
5Ukrainian (uk)
Теорема про сферу (диференціальна геометрія)
6.6709
More...

The following table shows the most popular language versions of the article.

Most popular in all the time

The most popular language versions of the article "Sphere theorem" in all the time
#LanguagePopularity awardRelative popularity
1English (en)
Sphere theorem
84 116
2German (de)
Sphärensatz
9 168
3Russian (ru)
Теорема о сфере (дифференциальная геометрия)
5 335
4French (fr)
Théorème de la sphère
3 071
5Ukrainian (uk)
Теорема про сферу (диференціальна геометрія)
193
More...

The following table shows the language versions of the article with the highest popularity in the last month.

Most popular in June 2025

The most popular language versions of the article "Sphere theorem" in June 2025
#LanguagePopularity awardRelative popularity
1English (en)
Sphere theorem
557
2German (de)
Sphärensatz
62
3Russian (ru)
Теорема о сфере (дифференциальная геометрия)
56
4French (fr)
Théorème de la sphère
25
5Ukrainian (uk)
Теорема про сферу (диференціальна геометрія)
4
More...

The following table shows the language versions of the article with the highest Authors’ Interest.

The highest AI

Language versions of the article "Sphere theorem" with the highest Authors Interest (number of authors). Only registered Wikipedia users were taken into account.
#LanguageAI awardRelative AI
1English (en)
Sphere theorem
24
2German (de)
Sphärensatz
19
3French (fr)
Théorème de la sphère
13
4Ukrainian (uk)
Теорема про сферу (диференціальна геометрія)
6
5Russian (ru)
Теорема о сфере (дифференциальная геометрия)
3
More...

The following table shows the language versions of the article with the highest Authors’ Interest in the last month.

The highest AI in June 2025

Language versions of the article "Sphere theorem" with the highest AI in June 2025
#LanguageAI awardRelative AI
1German (de)
Sphärensatz
0
2English (en)
Sphere theorem
0
3French (fr)
Théorème de la sphère
0
4Russian (ru)
Теорема о сфере (дифференциальная геометрия)
0
5Ukrainian (uk)
Теорема про сферу (диференціальна геометрія)
0
More...

The following table shows the language versions of the article with the highest number of citations.

The highest CI

Language versions of the article "Sphere theorem" with the highest Citation Index (CI)
#LanguageCI awardRelative CI
1English (en)
Sphere theorem
25
2German (de)
Sphärensatz
17
3French (fr)
Théorème de la sphère
10
4Russian (ru)
Теорема о сфере (дифференциальная геометрия)
9
5Ukrainian (uk)
Теорема про сферу (диференціальна геометрія)
4
More...

Scores

Estimated value for Wikipedia:
English:
Global:
Popularity in June 2025:
English:
Global:
Popularity in all years:
English:
Global:
Authors in June 2025:
English:
Global:
Registered authors in all years:
English:
Global:
Citations:
English:
Global:

Quality measures

Interwikis

#LanguageValue
deGerman
Sphärensatz
enEnglish
Sphere theorem
frFrench
Théorème de la sphère
ruRussian
Теорема о сфере (дифференциальная геометрия)
ukUkrainian
Теорема про сферу (диференціальна геометрія)

Popularity rank trends

Best Rank English:
#835522
09.2023
Global:
#1328782
09.2023

AI rank trends

Best Rank English:
#213325
02.2024
Global:
#236810
11.2010

Languages comparison

Important global interconnections (July 2024 – June 2025)

Wikipedia readers most often find their way to information on Sphere theorem from Wikipedia articles about Ricci flow, Riemannian geometry, Richard S. Hamilton, Simon Brendle and Richard Schoen. Whereas reading the article about Sphere theorem people most often go to Wikipedia articles on Sectional curvature, Sphere theorem, Fubini–Study metric, Exotic sphere and Marcel Berger.

Cumulative results of quality and popularity of the Wikipedia article

List of Wikipedia articles in different languages (starting with the most popular):

News from 12 August 2025

On 12 August 2025 in multilingual Wikipedia, Internet users most often read articles on the following topics: Cristiano Ronaldo, Wednesday, Georgina Rodríguez, ChatGPT, Weapons, Jenna Ortega, deaths in 2025, Taylor Swift, Miguel Uribe Turbay, 2025–26 UEFA Champions League.

In English Wikipedia the most popular articles on that day were: Weapons (2025 film), Danielle Spencer (American actress), Cristiano Ronaldo, Deaths in 2025, Taylor Swift, Wednesday (TV series), Superman (2025 film), Georgina Rodríguez, Coolie (2025 film), The Fantastic Four: First Steps.

About WikiRank

The WikiRank project is intended for automatic relative evaluation of the articles in the various language versions of Wikipedia. At the moment the service allows to compare over 44 million Wikipedia articles in 55 languages. Quality scores of articles are based on Wikipedia dumps from July, 2025. When calculating current popularity and AI of articles data from June 2025 was taken into account. For historical values of popularity and AI WikiRank used data from 2001 to 2025... More information