Higher-dimensional flying wing Steady Ricci Solitons

Abstract: 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 the unique 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. Our approach is based on constructing continuous families of smooth Ricci flows emanating from continuous families of spherical polyhedra. This is built upon a combination of a new stability result of Ricci flows with scaling invariant estimates and the method of Gianniotis-Schulze in regularizing manifolds with singularities.