3 papers
math.NA2024
Parallel transport on matrix manifolds and Exponential Action
Du Nguyen, Stefan Sommer
We express parallel transport for several common matrix Lie groups with a family of pseudo-Riemannian metrics in terms of matrix exponential and exponential actions. The metrics ar…
math.PR2024
Second-order differential operators, stochastic differential equations and Brownian motions on embedded manifolds
Du Nguyen, Stefan Sommer
We specify the conditions when a manifold M embedded in an inner product space E is an invariant manifold of a stochastic differential equation (SDE) on E, linking it with the noti…
math.AP2024
Families of costs with zero and nonnegative MTW tensor in optimal transport and the c-divergences
Du Nguyen
We study the information geometry of $\bcc$-divergences from families of costs of the form $\mathsf{c}(x, \barx) =\mathsf{u}(x^{\mathfrak{t}}\barx)$ through the optimal transport p…