20 citations · 75 across the 11 of their papers we have counts for
12 papers
Inverse mean curvature flow and Ricci-pinched three-manifolds
Gerhard Huisken, Thomas Koerber
Let be a complete, connected, non-compact Riemannian three-manifold with non-negative Ricci curvature satisfying for some $\…
On the evolution of hypersurfaces along their inverse spacetime mean curvature
Gerhard Huisken, Markus Wolff
We construct weak solutions for the evolution of hypersurfaces along their inverse space-time mean curvature in asymptotically flat maximal initial data sets. As the speed of the n…
Inverse mean curvature evolution of entire graphs
Panagiota Daskalopoulos, Gerhard Huisken
We study the evolution of strictly mean-convex entire graphs over by Inverse Mean Curvature flow. First we establish the global existence of starshaped entire graphs with sup…
A fully nonlinear flow for two-convex hypersurfaces
S. Brendle, G. Huisken
We consider a one-parameter family of closed, embedded hypersurfaces moving with normal velocity , where $λ_1 \leq \hdots…
Pseudo-Riemannian geometry in terms of multi-linear brackets
Joakim Arnlind, Gerhard Huisken
We show that the pseudo-Riemannian geometry of submanifolds can be formulated in terms of higher order multi-linear maps. In particular, we obtain a Poisson bracket formulation of…
Mean curvature flow with surgery of mean convex surfaces in
S. Brendle, G. Huisken
We define a notion of mean curvature flow with surgery for two-dimensional surfaces in with positive mean curvature. Our construction relies on the earlier work of H…
On the geometry of Kähler-Poisson structures
Joakim Arnlind, Gerhard Huisken
We prove that the Riemannian geometry of almost Kähler manifolds can be expressed in terms of the Poisson algebra of smooth functions on the manifold. Subsequently, Kähler-Poisson…
Multi linear formulation of differential geometry and matrix regularizations
Joakim Arnlind, Jens Hoppe, Gerhard Huisken
We prove that many aspects of the differential geometry of embedded Riemannian manifolds can be formulated in terms of multi linear algebraic structures on the space of smooth func…
On the classical geometry of embedded manifolds in terms of Nambu brackets
Joakim Arnlind, Jens Hoppe, Gerhard Huisken
We prove that many aspects of the differential geometry of embedded Riemannian manifolds can be formulated in terms of a multi-linear algebraic structure on the space of smooth fun…
Discrete curvature and the Gauss-Bonnet theorem
Joakim Arnlind, Jens Hoppe, Gerhard Huisken
For matrix analogues of embedded surfaces we define discrete curvatures and Euler characteristics, and a non-commutative Gauss--Bonnet theorem is shown to follow. We derive simple…
On the classical geometry of embedded surfaces in terms of Poisson brackets
Joakim Arnlind, Jens Hoppe, Gerhard Huisken
We consider surfaces embedded in a Riemannian manifold of arbitrary dimension and prove that many aspects of their differential geometry can be expressed in terms of a Poisson alge…
Ancient solutions to the Ricci flow with pinched curvature
S. Brendle, G. Huisken, C. Sinestrari
We show that any ancient solution to the Ricci flow which satisfies a suitable curvature pinching condition must have constant sectional curvature.