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arXiv · 2608.22748

Interior estimates and regularity for the scalar curvature equation in dimension 4

Zhenyu Fan·Ravi Shankar
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Abstract

We establish a priori interior curvature estimates for the scalar curvature equation in dimension 4. Our approach relies on the doubling method introduced by Shankar and Yuan [SY25]. Key to the proof are an a priori doubling inequality under a small gradient assumption and the Alexandrov regularity for viscosity solutions; the latter is obtained via a new iterative rotation argument. Furthermore, we establish interior regularity for $C^1$ viscosity solutions.

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Zhenyu Fan, Ravi Shankar. 2026-08-24. Interior estimates and regularity for the scalar curvature equation in dimension 4. https://arxiv.org/abs/2608.22748

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