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Travelling graphs for the forced mean curvature motion in an arbitrary space dimension
forced mean curvature movement eikonal equation Hamilton-Jacobi equations viscosity solution
2011/8/25
Abstract: We construct travelling wave graphs of the form $z=-ct+\phi(x)$, $\phi: x \in \mathbb{R}^{N-1} \mapsto \phi(x)\in \mathbb{R}$, $N \geq 2$, solutions to the $N$-dimensional forced mean curvat...
The Erdős-Ko-Rado theorem for twisted Grassmann graphs
The Erd˝ os–Ko–Rado theorem Distance-regular graph Twisted Grass-mann graph
2011/2/28
We present a “modern” approach to the Erd˝os–Ko–Rado theorem for Q-polynomial distance-regular graphs and apply it to the twisted Grass-mann graphs discovered in 2005 by van Dam and Koolen.
Relative Quasiconvexity using Fine Hyperbolic Graphs
Relative Quasiconvexity Fine Hyperbolic Graphs
2010/12/8
We provide a new and elegant approach to relative quasi-convexity for relatively hyperbolic groups in the context of Bowditch’s approach to relative hyperbolicity using cocompact actions on fine hy-pe...
Lack of Spectral Gap and Hyperbolicity in Asymptotic Erdös-Renyi Random Graphs
Spectral Gap Hyperbolicity Asymptotic Erdö s-Renyi Random Graphs
2010/12/14
In this work, we prove the absence of a spectral gap for the normalized Laplacian of the Erdos-Renyi random graph G(n; p) when p = d n for d > 1 as n ! 1. We also prove that for any positive the Er...
In this paper we introduce a new geometric ow | the hyperbolic gradient ow for graphs in the (n + 1)-dimensional Euclidean space Rn+1.
Lifting Tropical Curves in Space and Linear Systems on Graphs
Tropical Curves in Space Linear Systems Graphs
2010/12/2
Tropicalization is a procedure for associating a polyhedral complex to a subva-riety of an algebraic torus. We study the question on which graphs arise from tropicalizing algebraic curves. By using Ba...