Classification Theory of Riemannian Manifolds

Sario, Leo; Nakai, Mitsuru; Wang, Cecilia; Chung, Lung Ock

doi:10.1007/bfb0064417

Cited by 62 publications

(36 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Inside this polygon the integrand of eq. (4.10) is a square integrable function apart from the singularities at the points t = z, t = w. Hence it fulfills the existence conditions given in [7]. Moreover, remembering that…”

Section: The Maxwell Field Theory On a Riemann Surfacementioning

confidence: 58%

“…(2.25) to be valid on the boundary. Finally, additional problems can arise in constructing the biharmonic correlation functions G(z, w) on a noncompact manifold M [7]. In certain cases the direct construction of the propagator < A T z A T w > in the following way is preferable:…”

Section: Maxwell Field Theory On a Complex Backgroundmentioning

confidence: 99%

“…The strategy is to obtain the propagator on the complex plane in the limit ρ → ∞. At the boundary, |z| = ρ, there are many possible boundary conditions for G(z, w) [7], for example ϕ = △ z ϕ = 0 or ϕ = ∂ n ϕ = 0, where ∂ n denotes the inner normal derivative. However, in our case, we have to demand that the gauge fixing condition is true also at the boundary.…”

Section: The Maxwell Field Theory On a Flat Space-timementioning

confidence: 99%

“…(3.6), but it is easy to check that this limit does not exist. The difficulties we encounter are part of a more general problem in defining the propagator G(z, w) with given boundary conditions on a noncompact manifold [7]. Here we try to find the propagator of the vector fields.…”

Section: The Maxwell Field Theory On a Flat Space-timementioning

confidence: 99%

“…The biharmonic equations of motion for the scalar fields ϕ are solved on a disk and on the complex plane and the explicit form of the propagators is derived. The difficulties of defining the propagators on noncompact manifolds are pointed out [7].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Free and interacting 2D Maxwell field theory on conformally flat spacetimes

Ferrari¹

1993

Class. Quantum Grav.

View full text Add to dashboard Cite

The free Maxwell field theory is quantized in the Lorentz gauge on a two dimensional manifold M with conformally flat background metric. It is shown that in this gauge the theory is equivalent, at least at the classical level, to a biharmonic version of the bosonic string theory. This equivalence is exploited in order to construct in details the propagator of a Work supported by the Consiglio Nazionale Ricerche, P.le A. Moro 7, Roma, Italy

show abstract

Section: The Maxwell Field Theory On a Riemann Surfacementioning

confidence: 58%

Section: Maxwell Field Theory On a Complex Backgroundmentioning

confidence: 99%

Section: The Maxwell Field Theory On a Flat Space-timementioning

confidence: 99%

Section: The Maxwell Field Theory On a Flat Space-timementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Free and interacting 2D Maxwell field theory on conformally flat spacetimes

Ferrari¹

1993

Class. Quantum Grav.

View full text Add to dashboard Cite

show abstract

Stability of p‐parabolicity under quasi‐isometries

Granados

Pestana

Portilla

et al. 2022

Mathematische Nachrichten

View full text Add to dashboard Cite

Kanai proved the stability under quasi-isometries of numerous global properties (including existence of Green's function, i.e., non-parabolicity) between Riemannian manifolds of bounded geometry. Unfortunately, Kanai's hypotheses are not usually satisfied in the context of Riemann surfaces endowed with the Poincaré metric. In this work we prove the stability of 𝑝-parabolicity (with 1 < 𝑝 < ∞) by quasi-isometries, under hypotheses that many Riemann surfaces satisfy. Consequences for the stability of the Liouville property are obtained. In order to get our results, it is shown that each Riemannian surface with pinched negative curvature is bilipschitz equivalent to a surface with constant negative curvature.

show abstract

The Existence and Uniqueness of Solutions by the Covering Domain Method in Linear Elastostatics

Lin

Ballmann

1996

Z Angew Math Mech

View full text Add to dashboard Cite

The paper deals with problems of linear elastostatics with multiply connected solution domains. Generally, a multiply connected domain can be represented in a non‐unique way by the intersection set of n > 1 domains, each of which covering completely the original solution domain. If exact analytical solutions can be found in the covering domains, then, making use of the superposition principle, the solution of the original problem can be constructed by summation of the n solutions of the covering domains. Following this idea, the “covering Domain Method” is developed, by which the original problem is transformed into a system of Fredholm integral equations which finally offers the solution of the problem. In this paper we consider the existence and uniqueness of the solutions for different choice of covering domains. Two theorems are presented, which are useful for the application of the covering domain method in elasticity.

show abstract

Classification Theory of Riemannian Manifolds

Cited by 62 publications

References 0 publications

Free and interacting 2D Maxwell field theory on conformally flat spacetimes

Free and interacting 2D Maxwell field theory on conformally flat spacetimes

Stability of p‐parabolicity under quasi‐isometries

The Existence and Uniqueness of Solutions by the Covering Domain Method in Linear Elastostatics

Contact Info

Product

Resources

About