Related papers: Harder-Narasimhan theory
This note gives an informal overview of the proof in our paper "Borel Conjecture and Dual Borel Conjecture", see arXiv:1105.0823.
Under Wigdersons' framework and by sorting out the technical points in the recent works of Tang (J. Fourier Anal. Appl. 31 (2025)) and Dias-Luef-Prata (J. Math. Pures Appl. (9) 198 (2025)), we prove an abstract uncertainty principle for…
This paper concerns extension of the classical Lagrange theorem, on the eventual periodicity of continued fraction expansions of quadratic surds, and the versions of it found in the literature in the case of complex numbers. In this…
We have recently undergone an analysis of gravitational theories as defined in first order formalism, where the metric and the connection are treated as independent fields. The physical meaning of the connection field has historically been…
By adding the total time derivatives of all the constraints to the Lagrangian step by step, we achieve the further work of the Dirac conjecture left by Dirac. Hitherto, the Dirac conjecture is proved completely. It is worth noticing that…
We give a detailed proof for Gordan-Noether's results in "Ueber die algebraischen Formen, deren Hesse'sche Determinante identisch verschwindet" published in 1876 in Mathematische Annahlen. C. Lossen has written a paper in a similar…
An algebraic deformation theory of algebras over the Landweber-Novikov algebra is obtained.
We generalize the Lagrangian-Hamiltonian formalism of Skinner and Rusk to higher order field theories on fiber bundles. As a byproduct we solve the long standing problem of defining, in a coordinate free manner, a Hamiltonian formalism for…
We address the problem of the existence of a Lagrangian for a given system of linear PDEs with constant coefficients. As a subtask, this involves bringing the system into a pre-Lagrangian form, wherein the number of equations matches the…
Hamiltonian perturbation theory is used to analyse the stability of f(R) models. The Hamiltonian equations for the metric and its momentum conjugate are written for f(R) Lagrangian in the presence of perfect fluid matter. The perturbations…
This is an earlier, but more general, version of "An L^1 Ergodic Theorem for Sparse Random Subsequences". We prove an L^1 ergodic theorem for averages defined by independent random selector variables, in a setting of general…
As is known from studies of gravity models in the Palatini formalism, there exist two inequivalent definitions of the generalized Ricci tensor in terms of the generalized curvature namely, $\widetilde{R}_{\mu\nu}=R^\rho_{\mu\rho\nu}$ and…
This note is devoted to the study of Hamiltonian formalism of modified F(R) Horava-Lifshitz theories of gravity that were proposed recently in arXiv:1001.4102[hep-th]. We also study Hamiltonian formulation of the healthy extended…
In this survey, we review some of the low energy quantum predictions of General Relativity which are independent of details of the yet unknown high-energy completion of the gravitational interaction. Such predictions can be extracted using…
A general theory of summation of divergent series based on the Hardy-Kolmogorov axioms is developed. A class of functional series is investigated by means of ergodic theory. The results are formulated in terms of solvability of some…
We study the problem of interacting theories with (partially)-massless and conformal higher spin fields without matter in three dimensions. A new class of theories that have partially-massless fields is found, which significantly extends…
Approximations to the Kruskal-Katona theorem are stated and proven. These approximations are weaker than the theorem, but much easier to work with numerically.
This paper presents reflections on the validity of a series of mathematical methods and technical assumptions that are encrusted in macrophysics (related to gravitational interaction), that seem to have little or no physical significance.…
It is well-known that the equations for a simple fluid can be cast into what is called their Lagrange formulation. We introduce a notion of a generalized Lagrange formulation, which is applicable to a wide variety of systems of partial…
Algebraic dichotomy is a generalization of an exponential dichotomy (Lin, JDE2009). This paper gives a version of Hartman-Grobman linearization theorem assuming that linear system admits an algebraic dichotomy, which generalizes the…