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Dissipative Hyperbolic Geometric Flow
dissipative hyperbolic geometric flow quasilinear wave equation hyperbolic Ricci soliton short-time existence nonlinear stability
2018/4/20
In this paper we introduce a new kind of hyperbolic geometric flows — dissipative hyperbolic geometric flow. This kind of flow is defined by a system of quasilinear wave equations with dissipative ter...
The hyperbolic geometric flow on Riemann surfaces
hyperbolic geometric Riemann surface quasilinear hyperbolic system global existence blowup
2018/4/20
In this paper the authors study the hyperbolic geometric flow on Riemann surfaces. This new nonlinear geometric evolution equation was recently introduced by the first two authors motivated by Einstei...
Hyperbolic geometric flow (I): short-time existence and nonlinear stability
hyperbolic geometric °ow quasilinear hyperbolic equation strict hyperbolicity symmetric hyperbolic system nonlinear stability
2018/4/20
In this paper we establish the short-time existence and uniqueness theorem for hyperbolic geometric °ow, and prove the nonlinear stability of hyperbolic geometric °ow deˉned on the Euclidean space wit...
Wave character of metrics and hyperbolic geometric flow
Wave character metrics hyperbolic geometric flow
2018/4/20
In this letter, we illustrate the wave character of the metrics and curvatures of manifolds, and introduce a new understanding tool - the hyperbolic geometric °ow. This kind of °ow is new and very nat...