scholarly journals Spherical Metrics with Conical Singularities on a 2-Sphere: Angle Constraints

2015 ◽  
Vol 2016 (16) ◽  
pp. 4937-4995 ◽  
Author(s):  
Gabriele Mondello ◽  
Dmitri Panov
Keyword(s):  
Conical Singularities

scholarly journals Time-Harmonic Solutions for Maxwell’s Equations in Anisotropic Media and Bochner–Riesz Estimates with Negative Index for Non-elliptic Surfaces

2021 ◽  
Author(s):  
Rainer Mandel ◽  
Robert Schippa
Keyword(s):  
Gaussian Curvature ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Smooth Surfaces ◽  
Negative Index ◽  
Elliptic Surfaces ◽  
Conical Singularities ◽  
Fourier Restriction ◽  
Time Harmonic ◽  
Homogeneous Media

AbstractWe solve time-harmonic Maxwell’s equations in anisotropic, spatially homogeneous media in intersections of $$L^p$$ L p -spaces. The material laws are time-independent. The analysis requires Fourier restriction–extension estimates for perturbations of Fresnel’s wave surface. This surface can be decomposed into finitely many components of the following three types: smooth surfaces with non-vanishing Gaussian curvature, smooth surfaces with Gaussian curvature vanishing along one-dimensional submanifolds but without flat points, and surfaces with conical singularities. Our estimates are based on new Bochner–Riesz estimates with negative index for non-elliptic surfaces.

scholarly journals Krein Formula and S-Matrix for Euclidean Surfaces with Conical Singularities

2012 ◽  
Vol 23 (3) ◽  
pp. 1498-1529 ◽  
Author(s):  
Luc Hillairet ◽  
Alexey Kokotov
Keyword(s):  
Conical Singularities ◽  
S Matrix
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