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Huygens’ principle and equipartition of energy for the modified wave equation associated to a generalized radial Laplacian

Jamel El Kamel, Chokri Yacoub (2005)

Annales mathématiques Blaise Pascal

In this paper we consider the modified wave equation associated with a class of radial Laplacians L generalizing the radial part of the Laplace-Beltrami operator on hyperbolic spaces or Damek-Ricci spaces. We show that the Huygens’ principle and the equipartition of energy hold if the inverse of the Harish-Chandra c -function is a polynomial and that these two properties hold asymptotically otherwise. Similar results were established previously by Branson, Olafsson and Schlichtkrull in the case of...

Hyperbolic inverse mean curvature flow

Jing Mao, Chuan-Xi Wu, Zhe Zhou (2020)

Czechoslovak Mathematical Journal

We prove the short-time existence of the hyperbolic inverse (mean) curvature flow (with or without the specified forcing term) under the assumption that the initial compact smooth hypersurface of ℝ n + 1 ( n ≥ 2 ) is mean convex and star-shaped. Several interesting examples and some hyperbolic evolution equations for geometric quantities of the evolving hypersurfaces are shown. Besides, under different assumptions for the initial velocity, we can get the expansion and the convergence results of a hyperbolic...

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