Bochner formulas, functional inequalities and generalized Ricci flow
Bochner formulas, functional inequalities and generalized Ricci flow
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Bochner 公式、函数不等式和广义 Ricci 流
DOI：
10.1016/j.jfa.2023.109901
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发表时间：
2023
影响因子：
1.7
通讯作者：
Streets, Jeffrey
中科院分区：
文献类型：
--
作者：
Kopfer, Eva;Streets, Jeffrey
作为Bismut联络作用在梯度上的Bochner公式的结果，我们证明了广义Ricci流解的Poincaré不等式和log-Sobolev不等式沿着.使用两种形式的潜在的，我们定义了扭曲的时空连接，确定了一个适应布朗运动的框架丛，产生适应Malliavin梯度路径空间。我们证明了该算子的Bochner公式，从而得到了广义Ricci流的特征，并给出了相应的Malliavin梯度和Ornstein-Uhlenbeck算子的泛Poincaré和log-Sobolev型不等式。
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.