Robin and Neumann problems for the graph scalar curvature equation

Guohuan Qiu

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arXiv · 2608.21085

Robin and Neumann problems for the graph scalar curvature equation

Guohuan Qiu

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Abstract

We study Robin and Neumann problems for the scalar curvature equation of admissible graphs over bounded uniformly convex domains in three dimensions. Under a small-volume assumption, we prove existence and uniqueness for the Robin problem and obtain a classical Neumann solution as the Robin parameter tends to zero. The volume threshold is optimal among conditions depending only on the volume. The main step is a boundary second-derivative estimate uniform in the Robin parameter; known interior and global-to-boundary curvature estimates then give the global bound.

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Guohuan Qiu. 2026-08-21. Robin and Neumann problems for the graph scalar curvature equation. https://arxiv.org/abs/2608.21085

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