高维飞行翼稳态梯度Ricci溶iton
Higher-dimensional flying wing Steady Ricci Solitons
AI总结：
本文构造了高维稳态梯度Ricci溶iton，并扩展了飞行翼结构，提供了新的非负曲率算子例子，同时证明了扩展溶iton的稳定性。
摘要：
对于任何n≥4，我们构造了一个(n-2)参数族的稳态梯度Ricci溶iton，其曲率算子非负，并由溶iton势能临界点处Ricci张量的特征值所规定。其中包含一个(n-3)参数子族的非塌陷溶iton。这些溶iton扩展了由第二作者构造的飞行翼，并为n≥4提供了新的稳态梯度Ricci溶iton非负曲率算子的例子。我们的方法基于构造连续族的Ricci流，这些流平滑地从连续族的球面多面体出发，仍保持对称性。这建立在Ricci流的新稳定性结果之上，该结果具有缩放不变估计。作为该方法的另一应用，我们证明了由Deruelle构造的渐近锥形扩展溶iton在链接的L^∞扰动下是稳定的。特别是，光滑链接的C^0收敛性意味着扩展溶iton的光滑收敛性。
英文摘要：
For any $n\geq 4$, we construct an $(n-2)$-parameter family of steady gradient Ricci solitons with non-negative curvature operator and prescribed by the eigenvalues of Ricci tensor at a critical point of the soliton potential. Among them lies an $(n-3)$-parameter subfamily of non-collapsed solitons. These solitons generalized the flying wings constructed by the second named author and produced new examples of steady gradient Ricci solitons with non-negative curvature operator for $n\geq 4$. Our approach is based on constructing continuous families of Ricci flows smoothing emanating from continuous families of spherical polyhedra which still preserves symmetry. This is built upon a new stability result of Ricci flows with scaling invariant estimates. As another application of the method, we prove the stability of asymptotically conical expanding solitons constructed by Deruelle under $L^\infty$ perturbation of links. In particular, the $C^0$-convergence of smooth links implies the smooth convergence of the expanding solitons.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
