Subharmonic function

en

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Subharmonic function

Quality:

Subharmonic function - function f such that, if f≤h on the boundary of a ball for any harmonic function h, then f≤h also inside the ball. Article “Subharmonic function” in English Wikipedia has 21 points for quality (as of July 1, 2025). The article contains 2 references and 11 sections. The article also contains templates indicating quality issues, therefore its score was reduced by 1.11 points.

In this language version of Wikipedia the article has the best quality. Also, this article is the most popular in that (English) language version.

In June 2025 the article “Subharmonic function” was edited by 1 authors in English Wikipedia and written by 1 authors in all languages.

Since the creation of article “Subharmonic function”, its content was written by 33 registered users of English Wikipedia and edited by 102 registered Wikipedia users in all languages.

The article is cited 38 times in English Wikipedia and cited 110 times in all languages.

The highest Authors Interest rank from 2001:

  • Local (English): #128404 in November 2016
  • Global: #147721 in November 2007

The highest popularity rank from 2008:

  • Local (English): #472618 in December 2014
  • Global: #620604 in December 2014

There are 10 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
1English (en)
Subharmonic function
21.0432
2Catalan (ca)
Funció subharmònica
17.0473
3Finnish (fi)
Subharmoninen funktio
16.6937
4Russian (ru)
Субгармоническая функция
10.525
5Japanese (ja)
劣調和函数
9.4555
6Ukrainian (uk)
Субгармонічна функція
9.1765
7German (de)
Subharmonische Funktion
6.6071
8Italian (it)
Funzione subarmonica
4.3094
9French (fr)
Fonction sous-harmonique
3.1758
10Chinese (zh)
次调和函数
0.3998
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 "Subharmonic function" in all the time
#LanguagePopularity awardRelative popularity
1English (en)
Subharmonic function
215 764
2German (de)
Subharmonische Funktion
30 291
3French (fr)
Fonction sous-harmonique
14 178
4Russian (ru)
Субгармоническая функция
13 998
5Japanese (ja)
劣調和函数
12 324
6Italian (it)
Funzione subarmonica
6 702
7Chinese (zh)
次调和函数
5 828
8Finnish (fi)
Subharmoninen funktio
1 541
9Ukrainian (uk)
Субгармонічна функція
561
10Catalan (ca)
Funció subharmònica
43
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 "Subharmonic function" in June 2025
#LanguagePopularity awardRelative popularity
1English (en)
Subharmonic function
1 062
2Japanese (ja)
劣調和函数
182
3French (fr)
Fonction sous-harmonique
68
4German (de)
Subharmonische Funktion
61
5Italian (it)
Funzione subarmonica
56
6Chinese (zh)
次调和函数
44
7Russian (ru)
Субгармоническая функция
37
8Ukrainian (uk)
Субгармонічна функція
11
9Finnish (fi)
Subharmoninen funktio
10
10Catalan (ca)
Funció subharmònica
9
More...

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

The highest AI

Language versions of the article "Subharmonic function" with the highest Authors Interest (number of authors). Only registered Wikipedia users were taken into account.
#LanguageAI awardRelative AI
1English (en)
Subharmonic function
33
2German (de)
Subharmonische Funktion
19
3Russian (ru)
Субгармоническая функция
14
4French (fr)
Fonction sous-harmonique
10
5Italian (it)
Funzione subarmonica
8
6Finnish (fi)
Subharmoninen funktio
7
7Japanese (ja)
劣調和函数
4
8Ukrainian (uk)
Субгармонічна функція
4
9Chinese (zh)
次调和函数
2
10Catalan (ca)
Funció subharmònica
1
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 "Subharmonic function" with the highest AI in June 2025
#LanguageAI awardRelative AI
1English (en)
Subharmonic function
1
2Catalan (ca)
Funció subharmònica
0
3German (de)
Subharmonische Funktion
0
4Finnish (fi)
Subharmoninen funktio
0
5French (fr)
Fonction sous-harmonique
0
6Italian (it)
Funzione subarmonica
0
7Japanese (ja)
劣調和函数
0
8Russian (ru)
Субгармоническая функция
0
9Ukrainian (uk)
Субгармонічна функція
0
10Chinese (zh)
次调和函数
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 "Subharmonic function" with the highest Citation Index (CI)
#LanguageCI awardRelative CI
1English (en)
Subharmonic function
38
2French (fr)
Fonction sous-harmonique
14
3Japanese (ja)
劣調和函数
12
4Italian (it)
Funzione subarmonica
10
5Ukrainian (uk)
Субгармонічна функція
10
6Russian (ru)
Субгармоническая функция
9
7German (de)
Subharmonische Funktion
8
8Chinese (zh)
次调和函数
4
9Catalan (ca)
Funció subharmònica
3
10Finnish (fi)
Subharmoninen funktio
2
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
caCatalan
Funció subharmònica
deGerman
Subharmonische Funktion
enEnglish
Subharmonic function
fiFinnish
Subharmoninen funktio
frFrench
Fonction sous-harmonique
itItalian
Funzione subarmonica
jaJapanese
劣調和函数
ruRussian
Субгармоническая функция
ukUkrainian
Субгармонічна функція
zhChinese
次调和函数

Popularity rank trends

Best Rank English:
#472618
12.2014
Global:
#620604
12.2014

AI rank trends

Best Rank English:
#128404
11.2016
Global:
#147721
11.2007

Languages comparison

Important global interconnections (July 2024 – June 2025)

Wikipedia readers most often find their way to information on Subharmonic function from Wikipedia articles about Plurisubharmonic function, Potential theory, Harmonic function, Subharmonic series and Martingale. Whereas reading the article about Subharmonic function people most often go to Wikipedia articles on Harmonic function, Semi-continuity, Plurisubharmonic function, Maximum principle and Fine topology.

Cumulative results of quality and popularity of the Wikipedia article

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

News from 21 December 2025

On 21 December 2025 in multilingual Wikipedia, Internet users most often read articles on the following topics: Jeffrey Epstein, Anthony Joshua, James Ransone, Avatar: Fire and Ash, Jake Paul, Wake Up Dead Man, Stranger Things, Ghislaine Maxwell, Avatar, Avatar: The Way of Water.

In English Wikipedia the most popular articles on that day were: James Ransone, Avatar: Fire and Ash, Dhurandhar, Anthony Joshua, Jeffrey Epstein, .xxx, Jake Paul, Google Chrome, Epstein files, Chase DeMoor.

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