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A characterization of the Euclidean ball via antipodal points
Arising from an equilibrium state of a Fermi–Dirac particle system at the lowest temperature, a new characterization of the Euclidean ball is proved:...
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Some characterizations of the Euclidean ball
In this paper the following result is proved, which is an extension of the one proved in García-Jiménez et al. (Monatsh Math 181:601–607, 2016): a...
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The Euclidean Ball—The Drury Arveson Space
This chapter treats a commuting contractive tuple from the function theoretic point of view. This means introducing the Drury-Arveson space and...
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Spectral Decomposition of Discrepancy Kernels on the Euclidean Ball, the Special Orthogonal Group, and the Grassmannian Manifold
To numerically approximate Borel probability measures by finite atomic measures, we study the spectral decomposition of discrepancy kernels when...
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Boundary value problems in Euclidean space for bosonic Laplacians
A bosonic Laplacian is a conformally invariant second order differential operator acting on smooth functions defined on domains in Euclidean space...
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Spectral dimension, Euclidean embeddings, and the metric growth exponent
For reversible random networks, we exhibit a relationship between the almost sure spectral dimension and the Euclidean growth exponent, which is the...
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On the mean curvature type flow for convex capillary hypersurfaces in the ball
In this paper, we study the mean curvature type flow for hypersurfaces in the unit Euclidean ball with capillary boundary, which was introduced by...
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Locally Euclidean Metrics and their Isometric Realizations
There are many works related to metrics and surfaces of positive and negative curvature. This paper is a survey of results related to locally...
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Linear isoperimetric inequalities for free boundary submanifolds in a geodesic ball
We derive linear isoperimetric inequalities for free boundary submanifolds in a geodesic ball of a Riemannian manifold in terms of the modified...
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Nonlinear partial differential equations on noncommutative Euclidean spaces
Noncommutative Euclidean spaces—otherwise known as Moyal spaces or quantum Euclidean spaces—are a standard example of a non-compact noncommutative...
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The Critical Liouville Quantum Gravity Metric Induces the Euclidean Topology
We show that every possible metric associated with critical (γ = 2) Liouville quantum gravity (LQG) induces the same topology on the plane as the...
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Fourier Quasicrystals and Distributions on Euclidean Spaces with Spectrum of Bounded Density
We consider temperate distributions on Euclidean spaces with uniformly discrete support and locally finite spectrum. We find conditions on...
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New eigenvalue pinching results for Euclidean domains
We prove stability results associated with sharp eigenvalue upper bounds for several operators on embedded hypersurfaces and boundary problems on...
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Some extremal problems for polygons in the Euclidean plane
The paper is devoted to some extremal problems, related to convex polygons in the Euclidean plane and their perimeters. We present a number of...
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Pólya’s conjecture for Euclidean balls
The celebrated Pólya’s conjecture (1954) in spectral geometry states that the eigenvalue counting functions of the Dirichlet and Neumann Laplacian on...
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Nonsmooth Nonconvex Stochastic Heavy Ball
Motivated by the conspicuous use of momentum-based algorithms in deep learning, we study a nonsmooth nonconvex stochastic heavy ball method and show...
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Schwarz–Pick Estimates of the Real Unit Ball for Harmonic Map**s
In this paper, Schwarz–Pick estimates are obtained for harmonic map**s from the unit ball of ℝ n into origin-symmetric bounded convex domains Ω ⊂ ℝ m ,...
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Applications of ball spaces theory: fixed point theorems in semimetric spaces and ball convergence
In the paper, we apply some of the results from the theory of ball spaces in semimetric setting. This allows us to obtain fixed point theorems which...