AI 中文总结
该研究针对四维标量曲率方程，采用Shankar和Yuan[SY25]的加倍法，结合小梯度假设的先验加倍不等式与新迭代旋转论证，建立了内部曲率估计及C¹粘性解的内部正则性。
AI 中文摘要
我们建立了四维标量曲率方程的先验内部曲率估计，方法依赖Shankar和Yuan[SY25]提出的加倍法。证明的关键在于小梯度假设下的先验加倍不等式，以及粘性解的Alexandrov正则性，后者通过新的迭代旋转论证得到；此外，我们还建立了C¹粘性解的内部正则性。
英文摘要
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.
Comments38 pages
