Ohsawa–Takegoshi L2 extension theorem: Difference between revisions

Content deleted Content added

Inline

Revision as of 01:43, 3 October 2021

In several complex variables, the Ohsawa–Takegoshi L² extension theorem is a fundamental result concerning the holomorphic extension of a $L^{2}$ -holomorphic function defined on a bounded Stein manifold (such as a pseudoconvex compact set in $\mathbb {C} ^{n}$ of dimension less than $n$ ) to a domain of higher dimension, with a bound on the growth. It was discovered by Takeo Ohsawa and Kensho Takegoshi in 1987,^[1] using what have been described as ad hoc methods involving twisted Laplace–Beltrami operators, but simpler proofs have since been discovered.^[2] Many generalizations and similar results exist, and are known as theorems of Ohsawa-Takegoshi type.

References

^ Ohsawa, T.; Takegoshi, K. (1987). "On the extension of L2 holomorphic functions". Mathematische Zeitschrift. 195 (2): 197–204. doi:10.1007/BF01166457.
^ Siu, Y. T. (August 2011). "Section extension from hyperbolic geometry of punctured disk and holomorphic family of flat bundles". Science China Mathematics. 54 (8): 1767–1802. arXiv:1104.2563. Bibcode:2011ScChA..54.1767S. doi:10.1007/s11425-011-4293-7.

Guan, Qi'an; Zhou, Xiangyu (2015). "A solution of an $L^{2}$ extension problem with an optimal estimate and applications". Annals of Mathematics. 181 (3): 1139–1208. arXiv:1310.7169. doi:10.4007/annals.2015.181.3.6. JSTOR 24523356. S2CID 56205818.
Ohsawa, Takeo (2017). "On the extension of L2 holomorphic functions VIII — a remark on a theorem of Guan and Zhou". International Journal of Mathematics. 28 (9). doi:10.1142/S0129167X17400055.
Demailly, Jean-Pierre (2000). "On the Ohsawa-Takegoshi-Manivel L 2 extension theorem" (PDF). Complex Analysis and Geometry. pp. 47–82. doi:10.1007/978-3-0348-8436-5_3. ISBN 978-3-0348-9566-8.
Ohsawa, Takeo (10 December 2018). L2 Approaches in Several Complex Variables: Towards the Oka–Cartan Theory with Precise Bounds. Springer Monographs in Mathematics. doi:10.1007/978-4-431-55747-0. ISBN 9784431568513.

[OT1987-1] Ohsawa, T.; Takegoshi, K. (1987). "On the extension of L2 holomorphic functions". Mathematische Zeitschrift. 195 (2): 197–204. doi:10.1007/BF01166457.

[Siu2011-2] Siu, Y. T. (August 2011). "Section extension from hyperbolic geometry of punctured disk and holomorphic family of flat bundles". Science China Mathematics. 54 (8): 1767–1802. arXiv:1104.2563. Bibcode:2011ScChA..54.1767S. doi:10.1007/s11425-011-4293-7.

[1]

[2]

@@ Line 9: / Line 9: @@
 *{{cite journal |jstor=24523356|last1=Guan|first1=Qi'an|last2=Zhou|first2=Xiangyu|title=A solution of an <math>L^2</math> extension problem with an optimal estimate and applications|journal=Annals of Mathematics|year=2015|volume=181|issue=3|pages=1139–1208|doi=10.4007/annals.2015.181.3.6|s2cid=56205818|arxiv=1310.7169}}
 *{{cite journal |doi=10.1142/S0129167X17400055|title=On the extension of L2 holomorphic functions VIII — a remark on a theorem of Guan and Zhou|year=2017|last1=Ohsawa|first1=Takeo|journal=International Journal of Mathematics|volume=28|issue=9}}
+*{{cite book |doi=10.1007/978-3-0348-8436-5_3|chapter-url=https://www-fourier.ujf-grenoble.fr/~demailly/manuscripts/ohsawa_tak.pdf|chapter=On the Ohsawa-Takegoshi-Manivel L 2 extension theorem|title=Complex Analysis and Geometry|year=2000|last1=Demailly|first1=Jean-Pierre|pages=47–82|isbn=978-3-0348-9566-8}}
 *{{cite book |isbn=9784431568513|doi=10.1007/978-4-431-55747-0|title=L2 Approaches in Several Complex Variables: Towards the Oka–Cartan Theory with Precise Bounds|last1=Ohsawa|first1=Takeo|series=Springer Monographs in Mathematics|date=10 December 2018}}
 {{DEFAULTSORT:Ohsawa–Takegoshi L2 extension theorem}}
 [[Category:Mathematical theorems]]