Existence of solution to modified Gursky-Streets equation

Yi Huang; Zhenan Sui; Mingyu Xie

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arXiv · 2412.17437

Existence of solution to modified Gursky-Streets equation

Yi Huang·Zhenan Sui·Mingyu Xie

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Abstract

We solve the modified Gursky-Streets equation, which is a fully nonlinear equation arising in conformal geometry with uniform $C^{1, 1}$ estimates when (i) $\gamma > 0$ and $1 \leq k \leq n$ or (ii) $r > 0$ and $2 s k \leq r n$. We also prove the existence of a Lipschitz continuous viscosity solution when $r \neq 0$.

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Yi Huang, Zhenan Sui, Mingyu Xie. 2024-12-23. Existence of solution to modified Gursky-Streets equation. https://arxiv.org/abs/2412.17437

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