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Geodesics orbiting a singularity
We study the behaviour of geodesics on a Riemannian manifold near a generalized conical or cuspidal singularity. We show that geodesics entering a...
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A Family of Dicritical Foliations with One Singularity
We give an example of a family of dicritical foliations over the projective plane with one singularity and prove that it contains foliations with...
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Reconstructions of the Asymptotics of an Integral Determined by a Hyperbolic Unimodal Singularity
AbstractThe asymptotic behavior of an exponential integral is studied in which the phase function has the form of a special deformation of the germ...
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Singularity properties of Lorentzian Darboux surfaces in Lorentz–Minkowski spacetime
In this paper, by virtue of unfolding theory in singularity theory, we investigate the singularities of five special surfaces generated by a regular...
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The Singularity Set of Optimal Transportation Maps
AbstractOptimal transportation plays an important role in many engineering fields, especially in deep learning. By the Brenier theorem, computing...
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Integrable Cross-Field Generation Based on Imposed Singularity Configuration—The 2D Manifold Case
This work presents the mathematical foundations for the generation of integrable cross-field on 2D manifolds based on user-imposed singularity...
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The Singularity Theorems of General Relativity and Their Low Regularity Extensions
On the occasion of Sir Roger Penrose’s 2020 Nobel Prize in Physics, we review the singularity theorems of General Relativity, as well as their recent...
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Singularity Formation in an Incompressible Boundary Layer on an Upstream Moving Wall under Given External Pressure
AbstractThe two-dimensional laminar flow of a viscous incompressible fluid over a flat surface is considered at high Reynolds numbers. The influence...
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On Numerical Solution of a First Kind Integral Equation with a Weak Singularity in the Kernel on a Closed Surface
AbstractA direct method (self-regularization method) for the numerical solution of a weakly singular integral equation of the first kind on a closed...
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On the blow-up of a normal singularity at maximal Cohen–Macaulay modules
In Raynaud and Gruson (Invent Math 13:1–89, 1971) and Raynaud (Compos Math 24:11–31, 1972) developed the theory of blowing-up an algebraic variety X ...
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Contact Cylindrical Surfaces and a Projection of a Surface Around a Parabolic Point
We investigate differential geometric properties of a parabolic point of a surface in the Euclidean three space. We introduce the contact cylindrical...
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Singularity analysis for the V-notch in functionally graded piezoelectric/piezomagnetic material
The singularity of the V-notch in the functionally graded piezoelectric/piezomagnetic (FGPE/PM) material, whose property is varying as a power...
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Solutions with Power Type or Exponential Singularity for (3+1)-D Protter-Morawetz Problems
Transonic flows in fluid dynamics are modelled by mixed-type equations on the plane. On the other hand, M. H. Protter proposed multi-dimensional...
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The Probabilistic Method in Real Singularity Theory
We explain how to use the probabilistic method to prove the existence of real polynomial singularities with rich topology, i.e., with total Betti...
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Classification of Minimal Polygons with Specified Singularity Content
It is known that there are only finitely many mutation-equivalence classes with a given singularity content, and each of these equivalence classes...
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Singularity Theorems
Many solutions of the Einstein field equations, such as the Schwarzschild solution or the FLRW cosmological models, display singularities, beyond...
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On Angles between Linear Subspaces in \(\mathbb R^4\) and the Singularity
AbstractWe generalize the Khinchin singularity phenomenon for the problem in which, for a given irrational linear subspace, rational subspaces...
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Resolution of Surface Singularities
We introduce the notions of modification and resolution. In the presence of a resolution of a surface singularity we also define the exceptional...