arXiv research

The paper proves formulas and theorems for statistical de Rham Hodge operators on manifolds with boundary.

The paper studies perturbations of de Rham Hodge operators on manifolds with or without boundaries.

Promotes spectral functionals to noncommutative fields and proves a theorem.

Paper defines spectral triple and computes functional for nonminimal de Rham-Hodge operator.

New Lipschitz de Rham theorem for $L_p$-cohomology.

The paper proves a theorem related to gravitational action on manifolds.

Paper introduces a new multilinear functional for spectral triples and computes its properties.

We extend the study of the de Rham operator with ideal boundary conditions from the case of isolated conic singularities, as analyzed by Cheeger, to the case of arbitrary stratified pseudomanifolds. We introduce a class of ideal boundary operators and the notion of mezzoperversity, which intermediates between the stand…

We prove an analogue of the de Rham theorem for the extended L^2-cohomology introduced by M. Farber. This is done by establishing that the de Rham complex over a compact closed manifold with coefficients in a flat Hilbert bundle E of A-modules over a finite von Neumann algebra A is chain-homotopy equivalent (with bound…

Defines De Rham operator on diffeological spaces, showing it's unique.

Authors prove de Rham cohomology of Poisson and Jacobi manifolds is trivial.

New projection operators for multipatch spaces with stable properties.

Formulas derived for operators on forms in anti-de Sitter spaces.

Research resolves sign conventions in Floer theory for Morse-Bott case.

We are interested in the spectrum of the Hodge-de Rham operator on a cyclic covering $X$ over a compact manifold $M$ of dimension $n+1$. Let $Σ$ be a hypersurface in $M$ which does not disconnect $M$ and such that $M-Σ$ is a fundamental domain of the covering. If the cohomology group $H^{n/2 (Σ)$ is trivial, we can con…

Develops fractional de Rham theory for Maxwell equations.

Constructs a support-preserving homotopy for differential forms with boundary decay estimates.

The article characterizes a hemisphere using a Laplace operator and a differential equation.

Study polynomial structures on generalized tangent bundles and their compatibility with operators.

The paper extends Hodge-de Rham and Lichnérowicz Laplacians to double forms and proves vanishing theorems.

Algorithm computes eigenvalues and eigenforms on Calabi-Yau threefolds.

The Navier-Stokes equation on a Riemannian manifold is analyzed using Laplace operators.

Study cohomology of odd symplectic manifolds, linking to Lagrangian submanifolds and BV Laplacians.

We look at several problems in even dimensional conformal geometry based around the de Rham complex. A leading and motivating problem is to find a conformally invariant replacement for the usual de Rham harmonics. An obviously related problem is to find, for each order of differential form bundle, a ``gauge'' operator …

Two de Rham complexes in diffeology are compared using a factor map.

Unified method for analyzing evolving manifolds using de Rham-Hodge theory.

We introduce a weighted de Rham operator which acts on arbitrary tensor fields by considering their structure as r-fold forms. We can thereby define associated superpotentials for all tensor fields in all dimensions and, from any of these superpotentials, we deduce in a straightforward and natural manner the existence …

Unified mathematical theory for analyzing biomolecular geometry and flexibility.

Novel Hodge theory developed for Carrollian bundles, addressing black hole event horizons.

A C-infinity ring is a set equipped with n-ary operations corresponding to smooth n-ary functions on the real line (satisfying natural axioms). We prove that the cosimplicial abelian group associated to the de Rham complex of Euclidean space has the structure of a cosimplicial C-infinity ring. We also analyse the notio…

Study of de Rham cohomology on non-Hausdorff manifolds.

The paper explores de Rham theory for singular spaces and stacks.

Extended de Rham theorem for manifolds with boundaries.

Study reveals a link between Ruelle-Pollicott resonances and cohomology eigenvalues for Anosov diffeomorphisms.

Study de Rham homomorphism for Lipschitz cohomologies on metric simplicial complexes.

Study de Rham theory for cubical manifolds and quandles.

New path integrals for elasticity derived from differential complex theory.

Study describes global sections of chiral de Rham complex on compact Ricci-flat Kähler manifolds.

New cochain algebra for diffeological spaces connects de Rham and singular cohomologies.

Introduces differential forms to study inequalities between eigenvalues.

Study mapping class group action on de Rham quasimorphisms, finding no fixed points.

De Rham theorem extended to Orlicz cohomology.

New construction of Riemannian deformation sequence using differential operators.

New definition of de Rham spaces changes quotient structure.

Study proves formulas linking curvature to de Rham cohomology of foliations.

The Burde--de Rham theorem is extended to finitely presented pro-$p$ groups with specific conditions.

The primitive cohomology of Calabi-Yau intersections is described using a twisted de Rham complex.

This paper extends de Rham theory of smooth manifolds to exploded manifolds. Included are versions of Stokes' theorem, De Rham cohomology, Poincare duality, and integration along the fiber. The resulting cohomology theory is used to define Gromov Witten invariants of exploded manifolds in a separate paper.