论文标题
在超级歧管上的Quaternionic Monge-Ampere方程的尖锐均匀结合
Sharp uniform bound for the quaternionic Monge-Ampere equation on hyperhermitian manifolds
论文作者
论文摘要
我们为任何超级歧管上的Quaternion Monge-Ampere方程提供了尖锐的$ C^0 $估计。这改善了以前已知的有关该估计值的结果。也就是说，事实证明，估计仅取决于任何$ p> 2 $的右侧的$ l^p $ norm（如[SR20A]中研究的本地案例所建议）。此外，估计值仍然适用于任何超级精神的初始度量 - 无论它是HKT，就像[SR21]中作者所推测的Alesker -Verbitsky [AV10]的原始猜想中一样。为了完整性，我们实际上为许多Quaternionic PDE提供了一个尖锐的均匀估计，尤其是由操作员通过应用最近的Guo和Phong [GP22A]的方法来主导Quaternionic Monge-Ampere Operator的操作员。
We provide the sharp $C^0$ estimate for the quaternionic Monge-Ampere equation on any hyperhermitian manifold. This improves previously known results concerning this estimate in two directions. Namely, it turns out that the estimate depends only on $L^p$ norm of the right hand side for any $p>2$ (as suggested by the local case studied in [Sr20a]). Moreover, the estimate still holds true for any hyperhermitian initial metric - regardless of it being HKT as in the original conjecture of Alesker-Verbitsky [AV10] - as speculated by the author in [Sr21]. For completeness, we actually provide a sharp uniform estimate for many quaternionic PDEs, in particular those given by the operator dominating the quaternionic Monge-Ampere operator, by applying the recent method of Guo and Phong [GP22a].
