25 citations · 50 across the 15 of their papers we have counts for
15 papers
Spaces of metrics with positive spectral scalar curvature
Gioacchino Antonelli, Georg Frenck, Bernhard Hanke
Let and let be a closed connected smooth manifold. Let be the space of smooth Riemannian metrics on for which the generalized conformal Laplace oper…
Scalar Curvature Rigidity for Products of convex Hypersurfaces and even dimensional Manifolds
Georg Frenck, Thomas Schick, Lukas Schönlinner
We give a proof of scalar curvature rigidity in the spirit of Llarull and Goette-Semmelmann for products of strictly convex hypersurfaces in Euclidean space and nonnegatively curve…
The doubling conjecture for positive scalar curvature
Georg Frenck
The doubling conjecture predicts that a manifold admits positive scalar curvature with mean convex boundary if and only if its double admits positive scalar curvature. We show that…
The lock principle for scalar curvature
Georg Frenck, Bernhard Hanke, Sven Hirsch
We prove a Riemannian positive mass theorem for asymptotically flat spin manifolds with hypersurface singularities. Unlike earlier results, some components of the singular set may…
Surgery and total mean curvature
Georg Frenck, Bernhard Hanke, Sven Hirsch
We prove Gromov's conjecture on the total mean curvature of fill-ins in various cases. Our methods are based on surgery to reduce the statement to fill-ins of spheres, which can be…
Positive scalar curvature with point singularities
Simone Cecchini, Georg Frenck, Rudolf Zeidler
We show that in every dimension , there exists a smooth closed manifold which does not admit a smooth positive scalar curvature ("psc") metric, but admits an $\…
Spaces of Positive Scalar Curvature metrics on totally nonspin Manifolds with spin boundary
Georg Frenck
In this article we study the space of positive scalar curvature metrics on totally nonspin manifolds with spin boundary. We prove that for such manifolds of certain dimensions, tho…
Sphericity of -classes and positive curvature via block bundles
Georg Frenck
Given a simply connected manifold , we completely determine which rational monomial Pontryagin numbers are attained by fiber homotopy trivial -bundles over the -sphere, pr…
Diffeomorphisms and positive curvature
Georg Frenck
We prove the existence of elements of infinite order in the homotopy groups of the spaces and of positive Ricci and positive secti…
Spaces of positive intermediate curvature metrics
Georg Frenck, Jan-Bernhard Kordaß
In this paper we study spaces of Riemannian metrics with lower bounds on intermediate curvatures. We show that the spaces of metrics of positive p-curvature and k-positive Ricci cu…
Bundles with non-multiplicative -genus and spaces of metrics with lower curvature bounds
Georg Frenck, Jens Reinhold
We construct smooth bundles with base and fiber products of two spheres whose total spaces have non-vanishing -genus. We then use these bundles to locate non-trivial ratio…
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.
H-Space structures on spaces of metrics of positive scalar curvature
Georg Frenck
We construct and study an -space multiplication on for manifolds which are nullcobordant in their own tangential -type. This is applied to give a rigidi…
The action of the mapping class group on metrics of positive scalar curvature
Georg Frenck
We present a rigidity theorem for the action of the mapping class group on the space of metrics of positive scalar curvature for high dim…
The Gromov-Lawson-Chernysh surgery theorem
Johannes Ebert, Georg Frenck
In this article, we give a complete and self--contained account of Chernysh's strengthening of the Gromov--Lawson surgery theorem for metrics of positive scalar curvature. No claim…