We provide a quasilinear time algorithm for the p-center problem with an additive error less than or equal to 3 times the input graph’s hyperbolic constant. Specifically, for the graph G = (V,E) with n vertices, m edges and hyperbolic constant δ, we construct an algorithm for p-centers in time O(p(δ + 1)(n + m) log(n)) with radius not exceeding rp + δ when p ≤ 2 and rp + 3δ when p ≥ 3, where rp...

In this report we investigate the linear and nonlinear stability of stationary, constant solutions to the Cauchy problem of quasilinear, symmetric hyperbolic systems of equations. Writing the problem as u t = d X j=0 ? A 0j + "A 1j (x; t; u; ") with u(t = 0) = f(x); we say that the problem is non-linearly stable if, for " small enough, the solution u stays smooth for all t 0 and its maximum nor...

Using the maximal regularity theory for quasilinear parabolic systems, we prove two stability results of complex hyperbolic space under the curvature-normalized Ricci flow in complex dimensions two and higher. The first result is on a closed manifold. The second result is on a complete noncompact manifold. To prove both results, we fully analyze the structure of the Lichnerowicz Laplacian on co...