Bilaplacian on a Riemannian manifold and Levi-Civita connection

TL;DR

This paper extends the construction of Brownian motion on Riemannian manifolds to the Bilaplacian operator, providing a new geometric framework for higher-order differential operators.

Contribution

It introduces a generalized approach for the Bilaplacian on Riemannian manifolds, building upon the Eells-Elworthy-Malliavin construction for Brownian motion.

Findings

Established a geometric construction for Bilaplacian on manifolds

Extended stochastic methods to higher-order operators

Provided foundational tools for analysis on Riemannian manifolds

Abstract

We generalize for the Bilaplacian the Eells-Elworthy- Malliavin construction of the Brownian motion on a Riemannian manifold.