Topology-preserving Hodge Decomposition in the Eulerian Representation
Topology-preserving Hodge Decomposition in the Eulerian Representation
The Hodge decomposition is a fundamental result in differential geometry and algebraic topology, particularly in the study of differential forms on a Riemannian manifold. Despite extensive research in the past few decades, topology-preserving Hodge decomposition of scalar and vector fields on manifolds with boundaries in the Eulerian representation remains a …