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<p>In this paper, we present specific formulas for the Poisson kernels and Green’s functions for the triharmonic equation with three conformally invariant boundary conditions. As two applications, under proper growth control, we first classify positive solutions satisfying zero Q-curvature in the unit ball and constant T-curvature on the sphere with a singularity. Second, we establish two sharp geometric inequalities within the conformal class. This is a continuation of our earlier work [<CitationRef CitationID="CR13">13</CitationRef>].</p>

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The Poisson kernels for conformal boundary operators associated to the triharmonic equation and its applications

  • 期刊论文

  • 发表日期：

    2026年1月12日

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  • Shihong Zhang

摘要

In this paper, we present specific formulas for the Poisson kernels and Green’s functions for the triharmonic equation with three conformally invariant boundary conditions. As two applications, under proper growth control, we first classify positive solutions satisfying zero Q-curvature in the unit ball and constant T-curvature on the sphere with a singularity. Second, we establish two sharp geometric inequalities within the conformal class. This is a continuation of our earlier work [13].