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Goursat's problem and the holographic principle [PDF]
Nuclear Physics B, 2004 The whole idea of holography as put forward by Gerard 't Hooft assumes that data on a boundary determine physics in the volume. This corresponds to a Dirichlet problem for euclidean signature, or to a Goursat (characteristic) problem in the lorentzian setting. Is this last aspect of the problem that is explored here for Ricci flat spaces with vanishing
Álvarez, Enrique +2 more
openaire +4 more sources
Lightweight Curvature Estimation on Point Clouds with Randomized Corrected Curvature Measures
Computer Graphics Forum, Volume 42, Issue 5, August 2023., 2023 Abstract The estimation of differential quantities on oriented point cloud is a classical step for many geometry processing tasks in computer graphics and vision. Even if many solutions exist to estimate such quantities, they usually fail at satisfying both a stable estimation with theoretical guarantee, and the efficiency of the associated algorithm ...
J.‐O. Lachaud +4 more
wiley +1 more source
Monodromy of four‐dimensional irreducible compatible systems of Q$\mathbb {Q}$
Bulletin of the London Mathematical Society, Volume 55, Issue 4, Page 1773-1790, August 2023., 2023 Abstract Let F$F$ be a totally real field and n⩽4$n\leqslant 4$ a natural number. We study the monodromy groups of any n$n$‐dimensional strictly compatible system {ρλ}λ$\lbrace \rho _\lambda \rbrace _\lambda$ of λ$\lambda$‐adic representations of F$F$ with distinct Hodge–Tate numbers such that ρλ0$\rho _{\lambda _0}$ is irreducible for some λ0$\lambda ...
Chun Yin Hui
wiley +1 more source
Soil Deformation around a Cylindrical Cavity under Drained Conditions: Theoretical Analysis
Advances in Civil Engineering, Volume 2022, Issue 1, 2022., 2022 This paper proposes analytical solutions to the soil deformation around a cylindrical cavity under drained conditions. Analytical procedures are used to predict the degree of interaction between cavities and ground surface loads based on mathematical theorems.
Pieride Mabe Fogang +4 more
wiley +1 more source
Fractional Order Airy’s Type Differential Equations of Its Models Using RDTM
Mathematical Problems in Engineering, Volume 2021, Issue 1, 2021., 2021 In this paper, we propose a novel reduced differential transform method (RDTM) to compute analytical and semianalytical approximate solutions of fractional order Airy’s ordinary differential equations and fractional order Airy’s and Airy’s type partial differential equations subjected to certain initial conditions.
Daba Meshesha Gusu +4 more
wiley +1 more source
Trajectory generation for the N-trailer problem using Goursat normal form [PDF]
, 1995 Develops the machinery of exterior differential forms, more particularly the Goursat normal form for a Pfaffian system, for solving nonholonomic motion planning problems, i.e., motion planning for systems with nonintegrable velocity constraints.
Murray, Richard M. +2 more
core +2 more sources
Contact Geometry of Curves [PDF]
, 2009 Cartan's method of moving frames is briefly recalled in the context of immersed curves in the homogeneous space of a Lie group $G$. The contact geometry of curves in low dimensional equi-affine geometry is then made explicit.
Vassiliou, Peter J.
core +6 more sources
CONFORMAL SCATTERING AND THE GOURSAT PROBLEM
Journal of Hyperbolic Differential Equations, 2004 We work on a class of non-stationary vacuum space-times admitting a conformal compactification that is smooth at null and timelike infinity. Via a conformal transformation, the existence of a scattering operator for field equations is interpreted as the well-posedness of a Goursat problem on null infinity.
Mason, L, Nicolas, J
openaire +2 more sources
Conformal scattering on the Schwarzschild metric [PDF]
, 2015 We show that existing decay results for scalar fields on the Schwarzschild metric are sufficient to obtain a conformal scattering theory. Then we re-interpret this as an analytic scattering theory defined in terms of wave operators, with an explicit ...
Nicolas, Jean-Philippe
core +3 more sources
Inverse problems for general second order hyperbolic equations with time-dependent coefficients [PDF]
, 2017 We study the inverse problems for the second order hyperbolic equations of general form with time-dependent coefficients assuming that the boundary data are given on a part of the boundary.
Eskin, Gregory
core +2 more sources