Analytic characterization of equilateral triangles

DOI10.1007/s10231-021-01075-9zbMath1468.51010OpenAlexW3133141049MaRDI QIDQ2041500

Shigehiro Sakata

Publication date: 23 July 2021

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10231-021-01075-9

zbMATH Keywords

critical pointequilateral triangletriangle centerhot spotilluminating centerradial center

Mathematics Subject Classification ID

Continuity and differentiation questions (26B05) Elementary problems in Euclidean geometries (51M04) Euclidean analytic geometry (51N20) Miscellaneous topics in real functions (26E99)

Related Items (2)

Euclidean geometric description of radial centers of a triangle ⋮ Riesz-type inequalities and overdetermined problems for triangles and quadrilaterals

Cites Work

• Unnamed Item
• Renormalization of potentials and generalized centers
• Geometric heat comparison criteria for Riemannian manifolds
• Movement of hot spots over unbounded domains in \({\mathbb{R}}^ N\)
• Triangle centers as functions
• The spatial critical points not moving along the heat flow
• Looking for selectors of star bodies
• Every convex body has a unique illuminating center
• Geometric estimation of a potential and cone conditions of a body
• On heat conductors with a stationary hot spot
• Remarks on radial centres of convex bodies
• Movement of hot spots in Riemannian manifolds
• Movement of centers with respect to various potentials
• Regularized Riesz energies of submanifolds
• From electrostatic potentials to yet another triangle center
• Stationary radial centers and symmetry of convex polytopes

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