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In some previous papers the author gave an upper bound estimation for the Ricci curvature of a hypersurface in a hyperbolic space and in a sphere, see [4] and [5]. In the present paper, we give a lower bound estimation for the Ricci curvature of a compact connected embedded hypersurface in a hyperbolic space via the maximum principle given by H. Omori in [11].
. 44 149 176 Vincent, T. L., Van, M. V. and Goh, B. S. (1996): Ecological stability, evolutionary stability and the ESS maximum principle. Evol. Ecol
Abstract
In this paper we study optimal control problems for systems governed by nonlinear evolution equations. First we develop an existence theory for systems with a priori feedback using the reduction technique and a convexity-type hypothesis involving property Q. In doing this we also establish the nonemptiness of the set of admissible state-control pairs, by solving a nonlinear evolution inclusion. Then we obtain necessary conditions for optimality for a class of problems with terminal cost criterion and initial condition which is not a priori given but is only required to belong to a given set (systems with insufficient data in the terminology of Lions).
] Szarski , J. 1975 Strong maximum principle for non-linear parabolic differential-functional inequalities in arbitrary domain Ann. Polon. Math. 31 197 – 203
