Abstract

In this paper, first we prove the Crandall–Liggett exponential theorem in nonlinear semigroup theory on Hadamard manifolds. This theorem states that a semigroup of contractions can be constructed by the resolvent of a monotone vector field on Hadamard manifolds. Then, we show that the generated semigroup satisfies the evolution equation governed by the monotone vector field. The results of this paper are extensions of the classical results of Crandall and Liggett (Am J Math 93:265–298, 1971) and Brezis and Pazy (Israel J Math 8:367–383, 1970) to Hadamard manifolds. Some examples are also presented in the last part of the paper.