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October 17, 20250 citationsOpen Access

An existence theorem for non-pluripolar complex Monge-Ampère type equations on hyperconvex domains

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TDThai Duong DoNPNgoc Thanh Cong Pham

Key Points

  • An existence theorem demonstrates the solvability of complex Monge-Ampère equations in specified domains.
  • The study focuses on bounded hyperconvex domains in complex space, highlighting the significance of non-pluripolar measures.
  • Findings contribute theoretical insights into the relationship between singularities and the solutions of complex Monge-Ampère equations.
  • This research furthers understanding of geometric structures within complex geometry, as they relate to Monge-Ampère type equations.

Abstract

In this paper, we study the non-pluripolar complex Monge-Ampère measure on bounded domains in \ (Cⁿ \). We establish a general existence theorem for a non-pluripolar complex Monge-Ampère type equation with prescribed singularity on a bounded hyperconvex domain in \ (Cⁿ \).

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Cite This Study

Do et al. (2025) studied this question.

synapsesocial.com/papers/68f19f20de32064e504ddf3chttps://doi.org/10.48550/arxiv.2507.18116
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