多変数関数論4

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959: １３２人目の素数さん [sage] 2025/06/04(水) 10:12:18.08 ID:Vo5laslH

つづき

さて さらに
Yes, please more.

Copilotさんの回答2
Absolutely! Let's dive deeper.
(L^2)-Theory in Several Complex Variables
The (L^2)-method is a powerful tool in complex analysis, particularly in solving the (\bar{\partial})-equation.
This approach, pioneered by Lars Hörmander, provides existence theorems for holomorphic functions under certain curvature conditions. 1)
Recent research has refined the Oka–Cartan theory using (L2)-methods, leading to precise on hlomorphic extension. 2)
The Bergman kerenel, a fundamental object in complex analysis, has olso been extensively using L2-techniques.2)

Plurisubharmonic Functions
Plurisubharmonic functions are crucial in complex analysis and geometry.
They generalize subharmonic functions to multiple complex variables and play a key role in defining pseudoconvex domains.3)
These functions are used to study multiplier ideal sheaves, which have applications in algebraic geometry and singularity theory. 4)
The Levi problem, which characterizes domains of holomorphy, was historically solved using plurisubharmonic functions.3)
Would you like to explore specific applications or recent breakthroughs in these areas?
I can help break them down further!

参考
1)
https://www-fourier.ujf-grenoble.fr/~demailly/manuscripts/hormander_l2_estimates.pdf
Lars H¨ormander and the theory of L2 estimates for the ∂ operator Jean-Pierre Demailly

2)
https://link.springer.com/book/10.1007/978-4-431-56852-0
L² Approaches in Several Complex Variables
Towards the Oka–Cartan Theory with Precise Bounds
Authors: Takeo Ohsawa Book 2018

3)
https://en.wikipedia.org/wiki/Plurisubharmonic_function
Plurisubharmonic function

4)
https://www.math.ucdavis.edu/~hunter/m205b_18/projects/Plurisubharmonic_Functions.pdf
Plurisubharmonic Functions and Pseudoconvex Domains Thomas Jackson June 8, 2018

"Would you like to explore specific applications or recent breakthroughs in these areas?
I can help break them down further!"
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