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$𝒞^{k}$ -regularity for the $\bar{\partial}$ -equation with a support condition

Shaban Khidr, Osama Abdelkader (2017)

Czechoslovak Mathematical Journal

Let $D$ be a $𝒞^{d}$ $q$ -convex intersection, $d \geq 2$ , $0 \leq q \leq n - 1$ , in a complex manifold $X$ of complex dimension $n$ , $n \geq 2$ , and let $E$ be a holomorphic vector bundle of rank $N$ over $X$ . In this paper, $𝒞^{k}$ -estimates, $k = 2, 3, \dots, \infty$ , for solutions to the $\bar{\partial}$ -equation with small loss of smoothness are obtained for $E$ -valued $(0, s)$ -forms on $D$ when $n - q \leq s \leq n$ . In addition, we solve the $\bar{\partial}$ -equation with a support condition in $𝒞^{k}$ -spaces. More...

...-problem on weakly q-convex domains.

Lop-Hing Ho (1991)

Mathematische Annalen

ω-pluripolar sets and subextension of ω-plurisubharmonic functions on compact Kähler manifolds

Le Mau Hai, Nguyen Van Khue, Pham Hoang Hiep (2007)

Annales Polonici Mathematici

We establish some results on ω-pluripolarity and complete ω-pluripolarity for sets in a compact Kähler manifold X with fundamental form ω. Moreover, we study subextension of ω-psh functions on a hyperconvex domain in X and prove a comparison principle for the class 𝓔(X,ω) recently introduced and investigated by Guedj-Zeriahi.

Displaying 1 – 9 of 9

$𝒞^{k}$ -regularity for the $\bar{\partial}$ -equation with a support condition

...-problem on weakly q-convex domains.

ω-pluripolar sets and subextension of ω-plurisubharmonic functions on compact Kähler manifolds

Интегральные представления дифференциальных форм на многообразиях Коши-Римана и теория CR-функций. II

Нули голоморфных функций конечного порядка и весобые оценки решений $ø v e r l i n e \partial$ -уравнений

О $\bar{\partial}$ -задаче Неймана для гладких функций и распределений

О стирании особенностей интегрируемых CR-функций

Равномерные оценки решений $ø v e r l i n e \partial$ -уравнения в псевдовыпуклых полиэдрах

Решение с оценками $\bar{\partial}$ -уравнения в аналитических полиэдрах общего положения

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