GAUSS' DIVERGENCE THEOREM ON BOUNDED DOMAINS IN MINKOWSKI SPACES WITH APPLICATIONS TO HYPERBOLIC SIMPLICES.

For bounded domains of Euclidean spaces with piecewise smooth boundary, the integral of outward unit normal vectors of the boundary is zero. In this paper we consider a similar theorem on Minkowski spaces (Minkowski spaces does not mean finite dimensional Banach spaces but finite dimensional vector spaces with pseudo-inner products). We also consider Gauss' divergence theorem on Minkowski spaces, which implies above. Remark that this theorem implies easily the equation to calculate a kind of centroids of hyperbolic simplices. [ABSTRACT FROM AUTHOR]