Zobrazeno 1 - 10
of 165
pro vyhledávání: '"Zeriahi, Ahmed"'
We establish upper bounds on the diameter of compact K\"ahler manifolds endowed with K\"ahler metrics whose volume form satisfies an Orlicz integrability condition. Our results extend previous estimates due to Fu-Guo-Song, Y.Li, and Guo-Phong-Song-St
Externí odkaz:
http://arxiv.org/abs/2310.20482
Autor:
Badiane, Papa, Zeriahi, Ahmed
Let $1 \leq m \leq n$ be two integers and $\Omega \Subset \C^n$ a bounded $m$-hyperconvex domain in $\C^n$. Using a variational approach, we prove the existence of the first eigenvalue and an associated eigenfunction which is $m$-subharmonic with fin
Externí odkaz:
http://arxiv.org/abs/2306.04437
Autor:
Badiane, Papa, Zeriahi, Ahmed
Publikováno v:
Journal of Geometric Analysis, 33, Article number: 367 (2023)
We prove the existence of the first eigenvalue and an associated eigenfunction with Dirichlet condition for the complex Monge-Amp\`ere operator on a bounded strongly pseudoconvex domain in $\C^n$. We show that the eigenfunction is plurisubharmonic, s
Externí odkaz:
http://arxiv.org/abs/2306.03285
K\"ahler-Einstein currents, also known as singular K\"ahler-Einstein metrics, have been introduced and constructed a little over a decade ago. These currents live on mildly singular compact K\"ahler spaces $X$ and their two defining properties are th
Externí odkaz:
http://arxiv.org/abs/2305.12422
Autor:
Elaini, Hadhami, Zeriahi, Ahmed
Publikováno v:
Ann. Polon. Math. 2023
Let $1\leq m\leq n$ be two fixed integers. Let $\Omega \Subset \mathbb C^n$ be a bounded $m$-hyperconvex domain and $\mathcal A \subset \Omega \times ]0,+ \infty[$ a finite set of weighted poles. We define and study properties of the $m$-subharmonic
Externí odkaz:
http://arxiv.org/abs/2206.05527
Let $(V,\omega)$ be a compact K\"ahler manifold such that $V$ admits a cover by Zariski-open Stein sets with the property that $\omega$ has a strictly plurisubharmonic exhaustive potential on each element of the cover. If $X\subset V$ is an analytic
Externí odkaz:
http://arxiv.org/abs/2202.01325
In this note, we investigate some regularity aspects for solutions of degenerate complex Monge-Amp\`ere equations (DCMAE) on singular spaces. First, we study the Dirichlet problem for DCMAE on singular Stein spaces, showing a general continuity resul
Externí odkaz:
http://arxiv.org/abs/2012.02018
Autor:
Zeriahi, Ahmed
We introduce different classical characteristics used to regularize a subharmonic function and compare them. As an application we give a complete proof of a useful characterization of the modulus of continuity of such functions in terms of these char
Externí odkaz:
http://arxiv.org/abs/2007.08399
Autor:
Charabati, Mohamad, Zeriahi, Ahmed
Let $\Omega \subset \mathbb C^n$ be a bounded strictly $m$-pseudoconvex domain ($1\leq m\leq n$) and $\mu$ a positive Borel measure on $\Omega$. We study the Dirichlet problem for the complex Hessian equation $(dd^c u)^m \wedge \beta^{n - m} = \mu$ o
Externí odkaz:
http://arxiv.org/abs/2007.10194
Autor:
Benali, Amel, Zeriahi, Ahmed
Publikováno v:
Journal Ecole Polytechnique, Tome 7 (2020), 981-1007
Let $\Omega \Subset \mathbb C^n$ be a bounded strongly $m$-pseudoconvex domain ($1\leq m\leq n$) and $\mu$ a positive Borel measure with finite mass on $\Omega$. Then we solve the H\"older continuous subsolution problem for the complex Hessian equati
Externí odkaz:
http://arxiv.org/abs/2004.06952