Search arXivSearch

arXiv · math/0011262

The Generalized Metrical Multi-Time Lagrange Space of Relativistic Geometrical Optics

Abstract

The paper constructs a generalized metrical multi-time Lagrange space, which allows a natural development of relativistic geometrical optics theories, in a general setting.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Mircea Neagu. 2000-11-30. The Generalized Metrical Multi-Time Lagrange Space of Relativistic Geometrical Optics. https://arxiv.org/abs/math/0011262

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Degeneration of Riemann surfaces and small eigenvalues of the Laplacian

For a one-parameter degeneration of compact Riemann surfaces endowed with the Kähler metric induced from the Kähler metric on the total space of the family, we determine the exact magnitude of the small eigenvalues of the Laplacian as a function on the parameter space, under the assumption that the singular fiber is reduced. The novelty in our approach is that we compute the asymptotic behavior of certain difference of (logarithm of) analytic torsions in the degeneration in two ways. On the one hand, via heat kernel estimates, it is shown that the leading asymptotic is determined by the product of the small eigenvalues. On the other hand, using Quillen metrics, the leading asymptotic is connected with the period integrals, which we explicitly evaluate.

math.DG

Removable singularities of Yang-Mills-Higgs fields in higher dimensions

This paper establishes decay estimates near isolated singularities for $n$-dimensional Yang-Mills-Higgs fields defined on a fiber bundle ($n \geq 4$). These estimates yield a removable singularity theorem for Yang-Mills-Higgs fields under conformally invariant energy bounds, extending the classical results for Yang-Mills fields and harmonic maps.

math.DG

Improved Morse Index Stability for Sequences of Harmonic Maps from Degenerating Riemann Surfaces

We study the stability of the extended Morse index, defined as the number of negative and zero eigenvalues of the Jacobi operator, for sequences of harmonic maps on degenerating Riemann surfaces. As the conformal structure approaches the boundary of moduli space, collar collapse creates major analytical challenges. We analyze the second variation of the energy under these degenerations and identify conditions ensuring upper semicontinuity of the extended Morse index. Refining earlier results of the first and second authors in [7], we obtain sharper control of the spectrum of the Jacobi operator on degenerating domains. A key new aspect is the explicit contribution of geodesics arising as limits of the images of degenerating collars. We show that these neck regions converge to geodesic segments whose Morse index contributes nontrivially to the limiting extended index.

math.DG