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arXiv · 2405.11925

The Dirichlet problem for Monge-Amp\`ere type equations on Riemannian manifolds

Weisong Dong·Jinling Niu·Nadilamu Nizhamuding
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Abstract

In this paper, we study the Dirichlet problem for Monge-Amp\`ere type equations for $p$-plurisubharmonic functions on Riemannian manifolds. The $a$ $priori$ estimates up to the second order derivatives of solutions are established. The existence of a solution then follows by the continuity method.

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Weisong Dong, Jinling Niu, Nadilamu Nizhamuding. 2024-05-20. The Dirichlet problem for Monge-Amp\`ere type equations on Riemannian manifolds. https://arxiv.org/abs/2405.11925

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