Global BV entropy solutions to the Gauss–Codazzi system

The Gauss–Codazzi system for the given metric whose Gauss curvature is negative, is considered in the present paper. We provide some suitable conditions on the given metric such that the system admits a global BV entropy solution. Our main approach is applying the method of seeking global BV entropy solutions to the hyperbolic system of balance laws to the Gauss–Codazzi system. The global existence of BV solutions to the Gauss–Codazzi system yields a C1,1C1,1 isometric immersion of two dimensional manifold into R3R3.