论文标题
Bochner公式，功能不平等和普遍的RICCI流动
Bochner formulas, functional inequalities and generalized Ricci flow
论文作者
论文摘要
由于Bochner公式针对梯度作用于梯度，我们在通用RICCI流动的溶液中表现出尖锐的普遍庞加莱和Log-Sobolev的不平等。使用两种形式的电势，我们定义了时空上的扭曲连接，该连接确定了框架束上适应的布朗尼运动，从而在路径空间上产生了适应的Malliavin梯度。我们为该操作员展示了一个Bochner公式，从而导致了普遍的RICCI流动，以普遍的Poincaré和Log-Sobolev类型的不平等表示相关的Malliavin梯度和Ornstein-Uhlenbeck操作员。
As a consequence of the Bochner formula for the Bismut connection acting on gradients, we show sharp universal Poincaré and log-Sobolev inequalities along solutions to generalized Ricci flow. Using the two-form potential we define a twisted connection on spacetime which determines an adapted Brownian motion on the frame bundle, yielding an adapted Malliavin gradient on path space. We show a Bochner formula for this operator, leading to characterizations of generalized Ricci flow in terms of universal Poincaré and log-Sobolev type inequalities for the associated Malliavin gradient and Ornstein-Uhlenbeck operator.
