Suita conjecture explained
In mathematics, the Suita conjecture is a conjecture related to the theory of the Riemann surface, the boundary behavior of conformal maps, the theory of Bergman kernel, and the theory of the L2 extension. The conjecture states the following:
It was first proved by for the bounded plane domain and then completely in a more generalized version by . Also, another proof of the Suita conjecture and some examples of its generalization to several complex variables (the multi (high) - dimensional Suita conjecture) were given in and . The multi (high) - dimensional Suita conjecture fails in non-pseudoconvex domains.[1] This conjecture was proved through the optimal estimation of the Ohsawa–Takegoshi L2 extension theorem.
References
- 10.1007/s00222-012-0423-2. Suita conjecture and the Ohsawa-Takegoshi extension theorem. 2013. Błocki. Zbigniew. Inventiones Mathematicae. 193. 1. 149–158. 2013InMat.193..149B. 9209213. free.
- Book: 10.1007/978-3-319-09477-9_4. A Lower Bound for the Bergman Kernel and the Bourgain-Milman Inequality. [{{Google books|t6_CBAAAQBAJ|title=Geometric Aspects of Functional Analysis: Israel Seminar (GAFA) 2011-2013|page=52|plainurl=yes}} Geometric Aspects of Functional Analysis: Israel Seminar (GAFA) 2011-2013]. 2014a. Błocki. Zbigniew. Lecture Notes in Mathematics . 2116. 53–63. 978-3-319-09476-2.
- 10.1007/s13373-014-0058-2. Cauchy–Riemann meet Monge–Ampère. 2014b. Błocki. Zbigniew. Bulletin of Mathematical Sciences. 4. 3. 433–480. 53582451. free.
- Book: http://gamma.im.uj.edu.pl/~blocki/publ/mikael.pdf. 125704662 . 10.1007/978-3-319-52471-9_9 . Suita Conjecture from the One-dimensional Viewpoint . Analysis Meets Geometry . Trends in Mathematics . 2017 . Błocki . Zbigniew . 127–133 . 978-3-319-52469-6 .
- 10.1007/s12220-019-00343-8. Generalizations of the Higher Dimensional Suita Conjecture and Its Relation with a Problem of Wiegerinck. 2020. Błocki. Zbigniew. Zwonek. Włodzimierz. The Journal of Geometric Analysis. 30. 2. 1259–1270. 1811.02977. 119622596.
- 24523356. Guan. Qi'an. Zhou. Xiangyu. A solution of an
extension problem with optimal estimate and applications. Annals of Mathematics. 2015. 181. 3. 1139–1208. 10.4007/annals.2015.181.3.6. 56205818. 1310.7169.
- 10.4064/ap113-1-3. Two remarks on the Suita conjecture. 2015. Nikolov. Nikolai. Annales Polonici Mathematici. 113. 61–63. 1411.6601. 119147234.
- 10.1016/j.jmaa.2021.125018. Growth of Sibony metric and Bergman kernel for domains with low regularity. 2021. Nikolov. Nikolai. Thomas. Pascal J.. Journal of Mathematical Analysis and Applications. 499. 125018. 218581510. free. 2005.04479.
- Book: 10.1007/978-981-15-1588-0. [{{Google books|ssPXDwAAQBAJ|Bousfield Classes and Ohkawa's Theorem|page=426|plainurl=yes}} Bousfield Classes and Ohkawa's Theorem]. Springer Proceedings in Mathematics & Statistics. 2020. 309. 978-981-15-1587-3. 242194764.
- 10.1142/S0129167X17400055. On the extension of
holomorphic functions VIII — a remark on a theorem of Guan and Zhou. 2017. Ohsawa. Takeo. International Journal of Mathematics. 28. 9.
- 10.1007/BF00252460. Capacities and kernels on Riemann surfaces. 1972. Suita. Nobuyuki. Archive for Rational Mechanics and Analysis. 46. 3. 212–217. 1972ArRMA..46..212S. 123118650.
Notes and References
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