2025/04/25 by Leder, Roee · 1 citation
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2504.18494
We develop a framework for casting the solvability and uniqueness conditions of linearized geometric boundary-value problems in cohomological terms. The theory is designed to be applicable without assumptions on the underlying geometric structure and provides tools to study the emergent cohomology explicitly. To achieve this generality, we extend Hodge theory to sequences of Douglas--Nirenberg systems that interact via Green's formulae, overdetermined ellipticity, and a condition we call the order-reduction property, replacing the classical requirement that the sequence form a cochain complex. This property typically arises from linearized symmetries and constraints, as demonstrated in several examples, including exterior covariant derivatives, linearized prescribed Riemann curvature, and linearized Einstein equations with sources.