Harnack's inequality

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Harnack's inequality

Quality:

Harnack's inequality - theorem. Article “Harnack's inequality” in English Wikipedia has 14.5 points for quality (as of July 1, 2025). The article contains 0 references and 6 sections.

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

Since the creation of article “Harnack's inequality”, its content was written by 32 registered users of English Wikipedia and edited by 115 registered Wikipedia users in all languages.

The article is cited 21 times in English Wikipedia and cited 71 times in all languages.

The highest Authors Interest rank from 2001:

  • Local (English): #60511 in October 2005
  • Global: #70146 in June 2015

The highest popularity rank from 2008:

  • Local (English): #661483 in July 2021
  • Global: #960825 in July 2021

There are 14 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
1Turkish (tr)
Harnack eşitsizliği
27.5553
2English (en)
Harnack's inequality
14.4785
3Catalan (ca)
Desigualtat de Harnack
11.3281
4Korean (ko)
하르나크의 부등식
11.173
5Italian (it)
Disuguaglianza di Harnack
8.1953
6Ukrainian (uk)
Нерівність Гарнака
7.7283
7German (de)
Harnack-Ungleichung
6.7136
8Spanish (es)
Desigualdad de Harnack
6.1719
9Japanese (ja)
ハルナックの不等式
5.3717
10French (fr)
Inégalité de Harnack
3.8764
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 "Harnack's inequality" in all the time
#LanguagePopularity awardRelative popularity
1English (en)
Harnack's inequality
150 546
2Japanese (ja)
ハルナックの不等式
11 087
3German (de)
Harnack-Ungleichung
10 080
4Polish (pl)
Nierówność Harnacka
7 495
5Russian (ru)
Неравенство Гарнака
4 815
6Korean (ko)
하르나크의 부등식
4 485
7Vietnamese (vi)
Bất đẳng thức Harnack
4 192
8French (fr)
Inégalité de Harnack
3 863
9Spanish (es)
Desigualdad de Harnack
2 667
10Italian (it)
Disuguaglianza di Harnack
2 546
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 "Harnack's inequality" in June 2025
#LanguagePopularity awardRelative popularity
1English (en)
Harnack's inequality
810
2Japanese (ja)
ハルナックの不等式
150
3Russian (ru)
Неравенство Гарнака
50
4Italian (it)
Disuguaglianza di Harnack
34
5Spanish (es)
Desigualdad de Harnack
32
6German (de)
Harnack-Ungleichung
30
7French (fr)
Inégalité de Harnack
30
8Polish (pl)
Nierówność Harnacka
13
9Catalan (ca)
Desigualtat de Harnack
11
10Vietnamese (vi)
Bất đẳng thức Harnack
10
More...

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

The highest AI

Language versions of the article "Harnack's inequality" with the highest Authors Interest (number of authors). Only registered Wikipedia users were taken into account.
#LanguageAI awardRelative AI
1English (en)
Harnack's inequality
32
2German (de)
Harnack-Ungleichung
17
3Polish (pl)
Nierówność Harnacka
9
4Vietnamese (vi)
Bất đẳng thức Harnack
9
5Catalan (ca)
Desigualtat de Harnack
8
6Dutch (nl)
Ongelijkheid van Harnack
8
7Italian (it)
Disuguaglianza di Harnack
7
8French (fr)
Inégalité de Harnack
6
9Japanese (ja)
ハルナックの不等式
6
10Russian (ru)
Неравенство Гарнака
5
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 "Harnack's inequality" with the highest AI in June 2025
#LanguageAI awardRelative AI
1Catalan (ca)
Desigualtat de Harnack
0
2German (de)
Harnack-Ungleichung
0
3English (en)
Harnack's inequality
0
4Spanish (es)
Desigualdad de Harnack
0
5French (fr)
Inégalité de Harnack
0
6Italian (it)
Disuguaglianza di Harnack
0
7Japanese (ja)
ハルナックの不等式
0
8Korean (ko)
하르나크의 부등식
0
9Dutch (nl)
Ongelijkheid van Harnack
0
10Polish (pl)
Nierówność Harnacka
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 "Harnack's inequality" with the highest Citation Index (CI)
#LanguageCI awardRelative CI
1English (en)
Harnack's inequality
21
2German (de)
Harnack-Ungleichung
6
3Spanish (es)
Desigualdad de Harnack
6
4Italian (it)
Disuguaglianza di Harnack
6
5French (fr)
Inégalité de Harnack
5
6Japanese (ja)
ハルナックの不等式
5
7Korean (ko)
하르나크의 부등식
5
8Catalan (ca)
Desigualtat de Harnack
4
9Dutch (nl)
Ongelijkheid van Harnack
3
10Polish (pl)
Nierówność Harnacka
3
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
Desigualtat de Harnack
deGerman
Harnack-Ungleichung
enEnglish
Harnack's inequality
esSpanish
Desigualdad de Harnack
frFrench
Inégalité de Harnack
itItalian
Disuguaglianza di Harnack
jaJapanese
ハルナックの不等式
koKorean
하르나크의 부등식
nlDutch
Ongelijkheid van Harnack
plPolish
Nierówność Harnacka
ruRussian
Неравенство Гарнака
trTurkish
Harnack eşitsizliği
ukUkrainian
Нерівність Гарнака
viVietnamese
Bất đẳng thức Harnack

Popularity rank trends

Best Rank English:
#661483
07.2021
Global:
#960825
07.2021

AI rank trends

Best Rank English:
#60511
10.2005
Global:
#70146
06.2015

Languages comparison

Important global interconnections (July 2024 – June 2025)

Wikipedia readers most often find their way to information on Harnack's inequality from Wikipedia articles about Harmonic function, Harnacks principle, List of inequalities, David Jerison and Potential theory. Whereas reading the article about Harnack's inequality people most often go to Wikipedia articles on Harnacks principle, Poisson kernel, Carl Gustav Axel Harnack, Harmonic function and Grigori Perelman.

Cumulative results of quality and popularity of the Wikipedia article

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

News from 15 February 2026

On 15 February 2026 in multilingual Wikipedia, Internet users most often read articles on the following topics: Jeffrey Epstein, Wuthering Heights, 2026 Winter Olympics, Epstein files, Ilia Malinin, Wuthering Heights, Ghislaine Maxwell, Lucas Pinheiro Braathen, 2026 Winter Olympics medal table, Valentine's Day.

In English Wikipedia the most popular articles on that day were: Jeffrey Epstein, Wuthering Heights, Wuthering Heights (2026 film), 2026 Winter Olympics, Lucas Pinheiro Braathen, Ice hockey at the 2026 Winter Olympics – Men's tournament, Epstein files, John F. Kennedy Jr., Anthony Kim, James Van Der Beek.

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