https://neckpinch.com/authors/david-gonzalez-alvaro/New arXiv papers by David González-Álvaro, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2606.21417arxiv:2606.21417Fri, 19 Jun 2026 00:00:00 GMTJason DeVito, David González-Álvaro, Masoumeh Zarei — We prove that the Ricci flow preserves positive sectional curvature on homogeneous spheres and complex projective spaces. In conjunction with prior results, this completes the classification of which homogeneous spaces have positively curved metrics flowing outside the set of positively curved metrics and which do not.Ricci flowSphere theoremsHomogeneous spaces https://arxiv.org/abs/2403.13764arxiv:2403.13764Wed, 20 Mar 2024 00:00:00 GMTDavid González-Álvaro, Masoumeh Zarei — We prove that there exist SU₃-invariant metrics on Aloff-Wallach spaces W⁷_(k₁, k₂), as well as SU₅-invariant metrics on the Berger space B¹³, which have positive sectional curvature and evolve under the Ricci flow to metrics with non-positively curved planes.Ricci flowSphere theorems https://arxiv.org/abs/2303.08641arxiv:2303.08641Wed, 15 Mar 2023 00:00:00 GMTDavid González-Álvaro, Masoumeh Zarei — We show that, for any n≥ 2, there exists a homogeneous space of dimension d=8n-4 with metrics of Ric_(d/2-5)>0 if n≠ 3 and Ric₆>0 if n=3 which evolve under the Ricci flow to metrics whose Ricci tensor is not (d-4)-positive. Consequently, Ricci flow does not preserve a range of curvature conditions that interpolate between positive sectional and positive scalar curvature. This extends a theorem of Böhm and Wilking in the case of n=2.Ricci flowSphere theoremsScalar curvatureHomogeneous spaces