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On Solvability of Homological Equations in the Problem of Center Manifold Approximation
AbstractThe article considers the questions of the homological equations solvability that arise in the problem of center manifold approximations in...
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Center Manifold for the Third-Order Nonlinear Schrödinger Equation with Critical Lengths
This paper is concerned with the third-order nonlinear Schrödinger equation, a version of the center manifold theorem is established which is...
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Generalization of the Notion of Completeness of a Riemannian Analytic Manifold
In this paper, we discuss the concept of an analytic prolongation of a local Riemannian metric. We propose a generalization of the notion of...
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Reduction of Fibrations of a Grassmann-Like Manifold of Centered Planes Under Normalization
In the projective space P n , we consider the Grassmann-like manifold Gr ∗ ( m, n ) of centered planes and the associated principal fibration. We perform...
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A Grassmann manifold handbook: basic geometry and computational aspects
The Grassmann manifold of linear subspaces is important for the mathematical modelling of a multitude of applications, ranging from problems in...
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A collection of efficient retractions for the symplectic Stiefel manifold
This article introduces a new map on the symplectic Stiefel manifold. The operation that requires the highest computational cost to compute the novel...
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A class of inverse quotient curvature flow in the AdS-Schwarzschild manifold
In this paper, we study the asymptotic behavior of a class of inverse quotient curvature flow in the anti-de Sitter-Schwarzschild manifold. We prove...
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Periodic Center Manifolds for DDEs in the Light of Suns and Stars
In this paper, we prove the existence of a periodic smooth finite-dimensional center manifold near a nonhyperbolic cycle in classical delay...
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Schwarz lemma from a Kähler manifold into a complex Finsler manifold
Suppose that M is a complete Kähler manifold such that its holomorphic sectional curvature is bounded from below by a constant and its radial...
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Slow-Fast Systems with an Equilibrium Near the Folded Slow Manifold
We study a slow-fast system with two slow and one fast variables. We assume that the slow manifold of the system possesses a fold and there is an...
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Mass, center of mass and isoperimetry in asymptotically flat 3-manifolds
We revisit the interplay between the mass, the center of mass and the large scale behavior of certain isoperimetric quotients in the setting of...
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Some Criteria of Capacitive Type of a Noncompact Riemannian Manifold
AbstractA fairly general concept of an integral capacity on a Riemannian manifold is considered, which includes the concepts of capacity known for...
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Minkowski: The Universe Is a 4-Dimensional Manifold
In 1908 in a lecture Minkowski gave a brilliant reformulation of Einstein’s theory. He views the World as a 4-dimensional manifold that can be...
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Manifold Embeddings by Heat Kernels of Connection Laplacian
We show that any closed n -dimensional manifold ( M , g ) can be embedded by a map constructed using the heat kernels of the connection Laplacian as well...
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Uniformly strong convergence of Kähler-Ricci flows on a Fano manifold
In this paper, we study the uniformly strong convergence of the Kähler-Ricci flow on a Fano manifold with varied initial metrics and smoothly...
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Manifold and Orbifold Constructions
In this chapter, we collect some information on various constructions of manifolds, orbifolds, and their covers. Notably, we discuss the notions of...
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Generalization of a Theorem on the Equivalence of the Coordinate and Algebraic Definitions of a Smooth Manifold
In this paper, we generalize the theorem on the equivalence of the coordinate and algebraic definitions of a smooth manifold. Within the framework of...
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Classification of the Gluing Matrices on the Loop Molecules of the Points of Center-Center Type
The Fomenko–Zieschang theory of topological invariants says that the mark r is zero for the points of center-center type. The mark ε is known to be...