| Hyperbolic inverse curvature flow in recent years is one of the popular research fields in differential geometry.The research theory is closely to Riemannian geometry,partial differential equations,etc.Let M0 be a compact,mean convex,star—shaped smooth hypersurface of the n+1 dimensional warped product space Wnn+1(n≥2),which is given an embedding X0:Nn→Wn+1.We study the following initial value problem:#12where F defined on an open cone Γ is a function of principle curvature,v is the unit outward normal vector on X(x,t).X0 be a smooth function and X1 be a smooth vector-valued function on Nn.We prove the short time existence of the solution of this equation,and then calculate the evolution equations of some geometric quantities on the smooth hypersurfaces. |
