Asymptotic Estimates on the Time Derivative of Φ-entropy on Riemannian Manifolds

(整期优先)网络出版时间:2014-04-14
/ 1
Inthisnote,weobtainanasymptoticestimateforthetimederivativeoftheΦ-entropyintermsofthelowerboundoftheBakry–EmeryΓ2curvature.InthecasesofhyperbolicspaceandtheHeisenberggroup(moregenerally,thenilpotentLiegroupofranktwo),weshowthatthetimederivativeoftheΦ-entropyisnon-increasingandconcaveintimet,alsowegetasharpasymptoticboundforthetimederivativeoftheentropyinthesecases.