Shortest Peer-Review

Following is the list of journals listing in the alphabet order with the shortest peer-review that I have ever seen. If you know more, please drop me a comment below. Please take note that neither survey nor review article is considered in this situation.

1. Acta Mathematica
   http://www.springerlink.com/content/0001-5962/
2. Acta Mathematica Vietnamica
   http://link.springer.com/journal/40306
   The shortest is 12 days, check this paper by del Angel, Mueller-Stach, van Straten, and Zuo.
3. Advances in Calculus of Variations
   http://www.degruyter.com/view/j/acv
   The shortest is 14 days, check this paper by Ejiri and Micallef.
   BASED ON RECEIVING AND REVISING DAYS
4. Advances in Mathematics (AiM)
   http://www.sciencedirect.com/science/journal/aip/00018708
   The shortest is 3 days, check this paper by Ohta and Sturm.
   The runner up is 7 days, check this paper by Li and Nguyen.
5. American Journal of Mathematics (AJM)
   http://muse.jhu.edu/journals/ajm/
6. Annales de l’Institut Henri Poincare (C) Non Linear Analysis
   http://www.sciencedirect.com/science/journal/aip/02941449
   The shortest is 7 days, check this paper by Cagnettia, Gomesa, Mitakec and Tran.
   The runner up is 18 days, check this paper by Dolbeault and Toscani and this paper by Ignat, Nguyen, Slastikov, and Zarnescud.
7. Annales Henri Poincaré
   http://link.springer.com/journal/23
   The shortest is 0 days, check this paper by Friedrich.
8. Annali della Scuola Normale Superiore di Pisa (New series)
   http://annaliscienze.sns.it/index.php?page=OnlineIndex
   The shortest is 80 days, check this paper by Phuc.
9. Annali di Matematica Pura ed Applicata
   http://www.springerlink.com/content/108198/
   The shortest is 31 days, check this paper by Batkam and Colin.
10. Annals of PDE
    https://www.springer.com/journal/40818
    The shortest is 9 days, check this paper by Grenier and Nguyen.
11. Annals of Mathematics (AoM)
    http://annals.math.princeton.edu/
12. Archive for Rational Mechanics and Analysis (ARMA)
    http://www.springerlink.com/content/0003-9527/
    The shortest is 43 days, check this paper by Nam and Seiringer.
13. Bulletin des Sciences Mathématiques
    http://www.sciencedirect.com/science/journal/aip/00074497
    The shortest is 27 days, check this paper by Cotsiolis and Labropoulos.
14. Calculus of Variations and Partial Differential Equations
    https://www.springer.com/journal/526
    3 days, check this paper by Martin and Yao
    10 days, check this paper by Chang, Gursky, and Yang.
    28 days, check this paper by Ros-Oton and Serra.
15. Communications in Contemporary Mathematics (CCM)
    http://www.worldscientific.com/worldscinet/ccm
    The shortest is 19 days, check this paper by M.M. Fall and T. Weth.
    The runner-up is 27 days, check this paper by S.Y. Yolcu and T. Yolcu.
    The third place is 33 days, check this paper by Rong and Zhang.
16. Communications in Mathematical Physics (CMP)
    http://www.springerlink.com/content/100467/
    The shortest is 20 days, check this paper by Constantin, Tarfulea, and Vicol .
    The runner-up is 37 days, check this paper by Dybalski and Gérard.
    The third place is 43 days, check this paper by Galloway and Schoen and this paper by Hebey, Pacard, and Pollack.
17. Communications in Partial Differential Equations
    http://www.tandfonline.com/toc/lpde20/current
18. Communications on Pure and Applied Mathematics (CPAM)
    http://onlinelibrary.wiley.com/journal/10.1002/%28ISSN%291097-0312
    NO ACCEPTANCE DATE SHOWN
19. Comptes Rendus Mathematique
    http://www.sciencedirect.com/science/journal/aip/1631073X
    The shortest is 0 day, check this paper by Druet.
    The runner-up is 1 day, check this paper by Mawhina, Ortegab, and Robles-Pérezb.
20. Duke Mathematical Journal (DMJ)
    http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&page=past&handle=euclid.dmj
    The shortest is 11 days, check this paper by Franecki and Kapranov.
    The runner-up is 15 days, check this paper by Šilhavý.
    The third place is 28 days, check this paper by Lin and Rivière.
    The fourth place is about 31 days, check this paper by Farb, Lubotzky, and Minsky.
    NO ACCEPTANCE DATE SHOWN, ONLY REVISION DATE SHOWN
21. Geometric And Functional Analysis (GAFA)
    http://www.springerlink.com/content/1016-443x/
    The shortest is 28 days, check this paper by Alon and Bourgain.
    The runner-up is 42 days, check this paper by Bourgain, Dirksen, and Nelson.
    The third place is 45 days, check this paper by Bourgain and Guth.
    The fourth place is about 50 days, check this paper by Tao and Vu.
    (Ref.: a comment below.)
22. Indiana University Mathematics Journal
    http://www.iumj.indiana.edu/IUMJ/issues.php
23. International Journal of Mathematics
    http://www.worldscientific.com/worldscinet/ijm
    The shortest is 1 days, check this paper by Fang, Jiang, Lin, and Xu.
24. International Mathematics Research Notices
    http://imrn.oxfordjournals.org/content/by/year
    The shortest is 2 days, check this paper by Hang and Yang.
    The runner-up is 54 days, check this paper by Bourgain.
25. Inventiones Mathematicae
    http://www.springerlink.com/content/0020-9910/
    The shortest is 16 days, check this paper by Kim and Oh.
    The runner-up is 31 days, check this paper by Venerucci.
26. Journal de Mathématiques Pures et Appliquées (JMPA)
    http://www.sciencedirect.com/science/journal/aip/00217824
    NO ACCEPTANCE DATE SHOWN, ONLY AVAILABILITY DATE SHOWN
27. Journal für die reine und angewandte Mathematik (Crelle)
    http://www.degruyter.com/view/j/crll?aheadOfPrint
    The shortest is 66 days, check this paper by Tian and Zhu.
28. Journal of Differential Equations (JDE)
    http://www.sciencedirect.com/science/journal/aip/00220396
    The shortest is 43 days, check this paper by Byun, Ok, and Ryu.
29. Journal of Differential Geometry (JDG)
    http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&page=past&handle=euclid.jdg
    NO ACCEPTANCE DATE SHOWN
30. Journal of Functional Analysis (JFA)
    http://www.sciencedirect.com/science/journal/aip/00221236
    The shortest is 0 days, check this paper by Mendelson and Paouris.
    The runner-up is 2 days, check this paper by Bourgain and Bulut.
    The third place is  7 days, check this paper by Bidaut-Véron, Chasseigne, and Véron.
    The fourth place is 11 days, check this paper by Escobar and Garcia.
    The fifth place is 13 days, check this paper by Aubin.
31. Journal of Geometric Analysis
    http://www.springerlink.com/content/1050-6926/
32. Journal of Global Optimization
    http://link.springer.com/journal/10898
    The shortest is 0 days, check this paper by Colombo and Wolenski.
33. Journal of Mathematical Analysis and Applications
    http://www.sciencedirect.com/science/journal/aip/0022247X
34. Journal of Number Theory
    http://www.sciencedirect.com/science/journal/0022314X
    The shortest is 7 days, check this paper by Vinh.
35. Journal of the American Mathematical Society (JAMS)
    http://www.ams.org/publications/journals/journalsframework/jams
36. Journal of the European Mathematical Society (JEMS)
    http://www.ems-ph.org/journals/all_issues.php?issn=1435-9855
    NO ACCEPTANCE DATE SHOWN, ONLY REVISION DATE SHOWN
37. manuscripta mathematica
    http://www.springerlink.com/content/0025-2611/
38. Mathematical Research Letters
    http://intlpress.com/site/pub/pages/journals/items/mrl/_home/_main/index.html
    NO ACCEPTANCE DATE SHOWN
    
39. Mathematische Annalen
    http://www.springerlink.com/content/0025-5831/
40. Mathematische Zeitschrift
    http://www.springerlink.com/content/0025-5874/
41. Memoirs of the American Mathematical Society
    http://www.ams.org/publications/journals/journalsframework/memo
42. NoDEA: Nonlinear Differential Equations and Applications
    http://www.springerlink.com/content/1021-9722/
43. Nonlinear Analysis: Theory, Methods & Applications
    http://www.sciencedirect.com/science/journal/aip/0362546X
    The shortest is 0 day, check this paper by Garcia-Azoreroa, Manfredib, Perala, and Rossi.
    The runner-up is 9 days, check this paper by Chiron; but I guess there should have a paper having less than 9 days.
44. Proceedings of the American Mathematical Society
    http://www.ams.org/jourcgi/jrnl_toolbar_nav/proc_all
45. Publications Mathématiques de L’IHÉS
    http://www.springerlink.com/content/0073-8301/
46. Set-Valued and Variational Analysis
    http://link.springer.com/journal/11228
    The shortest is 1 day, check this paper by Bonnans and de la Vega
47. SIAM Journal on Mathematical Analysis
    http://epubs.siam.org/toc/sjmaah/current
48. The Taiwanese Journal of Mathematics
    http://journal.taiwanmathsoc.org.tw
    The shortest is 6 days, check this paper by Chen.
49. Transactions of the American Mathematical Society
    http://www.ams.org/jourcgi/jrnl_toolbar_nav/tran_all
50. Vietnam Journal of Mathematics
    http://link.springer.com/journal/10013
    The shortest is 11 days, check this paper by Phu.
    The runner-up is 49 days, check this paper by Loi.

I take this chance to acknowledge the contribution from

• Dr. Nguyen Thac Dung from the National Taiwan University;
• Mr. Nguyen Van Luong from the University of Padova;
• Mr. Duong Duc Lam from the University of Sussex;
• …

for their contribution to the list/record.