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This article reviews the Poisson problem and Poincaré lemmas related to the hyperbolic upper half-space. The goal is to derive explicit formulas for all potentials using the fundamental solution of the Laplace operator which can be constructed component-wise from the fundamental solution of the Leutwiler-Weinstein equation.

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Poisson Problem on Multivector Fields in Hyperbolic Upper Half-Space H3

  • 会议论文

  • 发表日期：

    2026年

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  • Heikki Orelma,
  • M. Manuela Rodrigues,
  • Nelson Vieira

摘要

This article reviews the Poisson problem and Poincaré lemmas related to the hyperbolic upper half-space. The goal is to derive explicit formulas for all potentials using the fundamental solution of the Laplace operator which can be constructed component-wise from the fundamental solution of the Leutwiler-Weinstein equation.