9 citations · 18 across the 16 of their papers we have counts for
16 papers
Local Topology of Riemannian Manifolds with Lower Intermediate Ricci Curvature Bounds
Philipp Reiser, Masoumeh Zarei
We prove a vanishing theorem for the local Betti numbers of closed, -dimensional Riemannian manifolds with a lower volume bound, an upper diameter bound, and a lower intermediat…
Free Circle Actions and Positive Ricci Curvature on Manifolds with the Cohomology Ring of
Philipp Reiser
We classify which of the 672 oriented diffeomorphism types of closed, simply-connected spin 7-manifolds with the cohomology ring of admit a free circle action. In a…
Ricci curvature and minimal hypersurfaces with large Betti numbers
Davi Maximo, Philipp Reiser, Daniele Semola
In any dimension we construct a sequence of closed -dimensional Riemannian manifolds with positive Ricci curvature admitting embedded two-sided minimal hypersurfa…
Surgery and positive Bakry-Émery Ricci curvature
Philipp Reiser, Francesca Tripaldi
We consider the problem of preserving weighted Riemannian metrics of positive Bakry-Émery Ricci curvature along surgery. We establish two theorems of this type: One for connected s…
Examples of tangent cones of non-collapsed Ricci limit spaces
Philipp Reiser
We give new examples of manifolds that appear as cross sections of tangent cones of non-collapsed Ricci limit spaces. It was shown by Colding-Naber that the homeomorphism types of…
Positive Ricci curvature on connected sums of fibre bundles
Philipp Reiser
We consider the problem of preserving positive Ricci curvature along connected sums. In this context, based on earlier work by Perelman, Burdick introduced the notion of core metri…
Positive Ricci Curvature on Twisted Suspensions
Philipp Reiser
The twisted suspension of a manifold is obtained by surgery along the fibre of a principal circle bundle over the manifold. It generalizes the spinning operation for knots and pres…
Positive intermediate Ricci curvature on connected sums
Philipp Reiser, David J. Wraith
We consider the problem of performing connected sums in the context of positive intermediate Ricci curvature. We show that such connected sums are possible if the manifold…
A generalization of the Perelman gluing theorem and applications
Philipp Reiser, David J. Wraith
We extend a positive Ricci curvature gluing theorem of Perelman to a range of positive intermediate curvature conditions, ranging from positive scalar curvature up to (and includin…
Free torus actions and twisted suspensions
Fernando Galaz-García, Philipp Reiser
We express the total space of a principal circle bundle over a connected sum of two manifolds in terms of the total spaces of circle bundles over each summand, provided certain con…
Positive Intermediate Ricci Curvature on Fibre Bundles
Philipp Reiser, David J. Wraith
We prove a canonical variation-type result for submersion metrics with positive intermediate Ricci curvatures. This can then be used in conjunction with surgery techniques to estab…
Metrics of Positive Ricci Curvature on Simply-Connected Manifolds of Dimension
Philipp Reiser
A consequence of the surgery theorem of Gromov and Lawson is that every closed, simply-connected 6-manifold admits a Riemannian metric of positive scalar curvature. For metrics of…
Intermediate Ricci curvatures and Gromov's Betti number bound
Philipp Reiser, David J. Wraith
We consider intermediate Ricci curvatures on a closed Riemannian manifold . These interpolate between the Ricci curvature when and the sectional curvature when…
Generalized Surgery on Riemannian Manifolds of Positive Ricci Curvature
Philipp Reiser
The surgery theorem of Wraith states that positive Ricci curvature is preserved under surgery if certain metric and dimensional conditions are satisfied. We generalize this theorem…
Cohomogeneity One Manifolds and Homogeneous Spaces of Positive Scalar Curvature
Georg Frenck, Fernando Galaz-Garcia, Philipp Reiser
We characterize cohomogeneity one manifolds and homogeneous spaces with a compact Lie group action admitting an invariant metric with positive scalar curvature.
Moduli Spaces of Metrics of Positive Scalar Curvature on Topological Spherical Space Forms
Philipp Reiser
Let be a topological spherical space form, i.e. a smooth manifold whose universal cover is a homotopy sphere. We determine the number of path components of the space and moduli…