4 papers
Degenerations of exotic Calabi-Yau metrics through Atiyah's flop
Thibault Langlais, Viktor F. Majewski
We construct new families of complete Calabi-Yau metrics with maximal volume growth on the small resolutions of the conifold $\mathcal{Z} = \{z_1^2 + z_2^2 + z_3^2 + z_4^2 = 0\} \s…
Non-Existence of Smooth Full-Holonomy Cayley Fibrations
Jianfeng Lin, Viktor F. Majewski, Jacek Rzemieniecki
We prove that every Cayley fibration of a compact torsion-free Spin(7)-manifold with full holonomy must have singular fibers. This confirms a long-standing expectation in the study…
Spin(7)-Orbifold Resolutions
Viktor F. Majewski
We develop an analytic and geometric framework for resolving compact Spin(7)-orbifolds by smooth torsion-free Spin(7)-manifolds. These orbifolds arise naturally as boundary points…
Dirac Operators on Orbifold Resolutions: Uniform Elliptic Theory
Viktor F. Majewski
We study Dirac operators on resolutions of Riemannian orbifolds by developing a uniform elliptic theory. The key idea is to view orbifolds as conically fibred singular (CFS) spaces…