Related papers: Lectures on the fourth order Q curvature equation
The problem of equivalency for linear differential operators of the first order is discussed.
We consider an inverse variational problem for the lines of constant curvature in (pseudo-)Euclidean two-, three-, and four-dimensional spaces. The accumulated results are physically meaningful in the case of relativistic mechanics of…
This lecture presents recent advances in the theory of errors propagation. We first explain in which cases the propagation of errors may be performed with a first order differential calculus or needs a second order differential calculus.…
We consider a $4$-dimensional Riemannian manifold $M$ equip\-ped with a circulant structure $q$, which is an isometry with respect to the metric $g$ and $q^{4}=\id$, $q^{2}\neq \pm \id$. For such a manifold $(M, g, q)$ we obtain some…
For any hypersurface of a Riemannian manifold, recent works introduced the notions of extrinsic conformal Laplacians and extrinsic Q-curvatures. Here we announce explicit formulas for the extrinsic Paneitz operators P_4 and the…
This talk reviews some recent trends in perturbative quantum chromodynamics, with emphasis on higher orders in perturbation theory, resummation and power corrections.
We take a third-order approach to the fourth Painlev\'e equation and indicate the value of such an approach to other second-order ODEs in the Painlev\'e-Gambier list of 50.
Extensions of standard one-dimensional supersymmetric quantum mechanics are discussed. Supercharges involving higher order derivatives are introduced leading to an algebra which incorporates a higher order polynomial in the Hamiltonian. We…
In this study, after introducing algebraic properties of real quaternions some characterizations of quaternionic involute-evolute curves in Q are obtained. And some results and theorems for quaternionic w-curves are given. Lastly, we…
In this paper we prove a positive energy theorem related to fourth-order gravitational theories, which is a higher-order analogue of the classical ADM positive energy theorem of general relativity. We will also show that, in parallel to the…
The review of modern study of algebraic, geometric and differential properties of quaternionic (Q) numbers with their applications. Traditional and "tensor" formulation of Q-units with their possible representations are discussed and groups…
We study the higher order q- Poincar\'e and other coercive inequalities for a class probability measures satisfying Adam's regularity condition.
In the conformal class of Euclidean space, we give some volume comparison theorems with help of Q-curvature. Meanwhile, for compact four dimensional manifolds with non-negative scalar curvature, we give a volume rigidity theorem with…
A simplified, user-friendly repackaging of the curvature estimates implied by the Seiberg-Witten equations is formulated in terms of the convex hull of the set of monopole classes. New results are also obtained concerning boundary cases of…
Linearization problem of ordinary differential equations by a new set of tangent transformations is considered in the paper. This set of transformations allows one to extend the set of transformations applied for the linearization problem.…
This short article is a brief account of the usage of fourth-order curvature flow in surface modelling.
This note is devoted to study the implications of nonpositive isotropic curvature and negative Ricci curvature for Einstein $4-$Manifolds.
A systematic study of non-trivial cubic extensions of the four-dimensional Poincar\'e algebra is undertaken. Explicit examples are given with various techniques (Young tableau, characters etc).
The topics covered by the lectures include Symanzik's effective continuum theory, O(a) improvement, chiral symmetry on the lattice and non-perturbative renormalization.
I give a pedagogical introduction to the concepts and the tools that are necessary to study particle physics models in higher dimensions. I then give a more detailed presentation of warped compactifications and discuss their possible…