Björn JawerthDept. of Mathematics, Washington UniversityRichard RochbergDept. of Mathematics, Washington UniversityGuido WeissDept. of Mathematics, Washington University
We prove the Poincaré inequality for vector fields on the balls of the control distance by integrating along subunit paths. Our method requires that the balls are representable by means of suitable “controllable almost exponential maps”.
Chun-Lei CaoInstitute of Mathematics Academy of Mathematics and System Sciences, Chinese Academy of SciencesYue-Fei WangInstitute of Mathematics Academy of Mathematics and System Sciences, Chinese Academy of Sciences
Completely invariant components of the Fatou sets of meromorphic maps are discussed. Positive answers are given to Baker’s and Bergweiler’s problems that such components are the only Fatou components for certain classes of meromorphic maps.