复流形上k-Hessian方程的Dirichlet问题

IF 1.7 1区数学 Q1 MATHEMATICS

American Journal of Mathematics Pub Date : 2019-09-01 DOI:10.1353/ajm.2022.0040

Tristan C. Collins, Sebastien Picard

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引用次数: 17

摘要

文摘：在有边界的紧致复流形上，在存在亚解的情况下，我们求解$k$-Hessian方程的Dirichlet问题。我们的方法基于对具有特定梯度尺度的边界上的解的二阶先验估计。规模允许我们应用爆破论点来控制解决方案的所有必要规范。

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The Dirichlet problem for the k-Hessian equation on a complex manifold

abstract:We solve the Dirichlet problem for $k$-Hessian equations on compact complex manifolds with boundary, given the existence of a subsolution. Our method is based on a second order a priori estimate of the solution on the boundary with a particular gradient scale. The scale allows us to apply a blow-up argument to obtain control on all necessary norms of the solution.

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来源期刊

American Journal of Mathematics 数学-数学

CiteScore

3.20

自引率

0.00%

发文量

审稿时长

24 months

期刊介绍： The oldest mathematics journal in the Western Hemisphere in continuous publication, the American Journal of Mathematics ranks as one of the most respected and celebrated journals in its field. Published since 1878, the Journal has earned its reputation by presenting pioneering mathematical papers. It does not specialize, but instead publishes articles of broad appeal covering the major areas of contemporary mathematics. The American Journal of Mathematics is used as a basic reference work in academic libraries, both in the United States and abroad.