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An elementary proof of the Loomis–Whitney theorem
Loomis and Whitney proved an inequality between volume and areas of projections of an open set in n -dimensional space related to the...
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Some Regular Properties of the Hewitt–Stromberg Measures with Respect to Doubling Gauges
The aim of this paper is to show that if the Hewitt–Stromberg pre-measures with respect to the gauge are finite, then these pre-measures have a kind...
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A Note about Minimal Hypercones
This short note is concerned with a measure version criterion for hypersurfaces to be minimal. Certain natural flows and associated reflections for...
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Removable Singularities for Solutions of the Fractional Heat Equation in Time Varying Domains
In this paper we study removable singularities for solutions of the fractional heat equation in the spacial-time space. We introduce associated...
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Erdélyi–Kober Fractional Integrals and Radon Transforms for Mutually Orthogonal Affine Planes
We apply Erdélyi–Kober fractional integrals to the study of Radon type transforms that take functions on the Grassmannian of j -dimensional affine...
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Ahlfors-regular curves and Carleson measures
We study the relation between the boundary of a simply connected domain Ω being Ahlfors-regular and the invariance of Carleson measures under the...
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A note on the Blaschke-Petkantschin formula, Riesz distributions, and Drury’s identity
The Blaschke-Petkantschin formula is a variant of the polar decomposition of the k -fold Lebesgue measure on ℝ n in terms of the corresponding measures...
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A New Elliptic Measure on Lower Dimensional Sets
The recent years have seen a beautiful breakthrough culminating in a comprehensive understanding of certain scale-invariant properties of n − 1...
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Menshov’s “adjustment theorem” with respect to general measures
We prove Menshov’s theorem in the setting of arbitrary Borel measures.
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A Kind of New Continued Fraction Approximation of Gamma Function Based on Mortici’s Formula
In this paper, based on Mortici’s works, we establish two sharp general continued fraction approximations for the gamma function. Then related...
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On Lawson’s area-minimizing hypercones
We show the area-minimality property of all homogeneous area-minimizing hypercones in Euclidean spaces (classified by Lawlor) following Lawson’s...
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Isoperimetric, Sobolev, and eigenvalue inequalities via the Alexandroff-Bakelman-Pucci method: A survey
This paper presents the proof of several inequalities by using the technique introduced by Alexandroff, Bakelman, and Pucci to establish their ABP...