Ledrappier and Shu show that the linear drift of the Brownian motion on the universal cover of a closed connected smooth Riemannian manifold is Ck-2 differentiable along any Ck curve in the manifold of Ck Riemannian metrics with negative sectional curvature. They also show that the stochastic entropy of the Brownian motion is C1 differentiable along any C3 curve of C Riemannian metrics with negative sectional curvature. They formulate the first derivatives of the linear drift and stochastic entropy, respectively, and show that they are critical at locally symmetric metrics. Annotation ©2022 Ringgold, Inc., Portland, OR (protoview.com)
