4 papers
Metric mean dimension and the variational principle for actions of amenable groups
Rui Yang, Xiaoyao Zhou
Metric mean dimension is a dynamical counterpart of the box dimension in fractal geometry to characterize the topological complexity of infinite entropy systems. The classical vari…
Mean dimension and rate-distortion function revisited
Rui Yang
Around the mean dimensions and rate-distortion functions, using some tools from local entropy theory this paper establishes the following main results: We prove that for non-…
Hessian matrix estimates of heat-type equations via Bismut-Stroock Hessian formula
Li-Juan Cheng, Rui-Yu Yang
In this paper, we establish a new global Hessian matrix estimate for heat-type equations on Riemannian manifolds using a Bismut-type Hessian formula. Our results feature fully expl…
On the metric mean dimensions of saturated sets
Yong Ji, Junye Li, Rui Yang
From a geometric perspective, we employ metric mean dimension to investigate the set of generic points of invariant measures and saturated sets in infinite entropy systems. For sys…