Certain Gradient Flows and Submanifolds in Wiener Spaces

In Malliavin calculus, submanifolds in Wiener spaces have been studied by many people instead of loop spaces. For such submanifolds, we show the existence of the tabular neighborhoods, which are basic tools to study the properties of the differential operators on the submanifolds. To this end, it is crucial to show the existence and the regularity of the solutions to certain ordinary differential equations in Wiener spaces. As an application, we show the continuity of the divergence operators on submanifolds.