Analytic characterization of equilateral triangles

Sakata, Shigehiro

doi:10.1007/s10231-021-01075-9

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2021

2022

Publication Types

Select...

Other1

Article1

Relationship

Self Cite0

Independent2

Authors

Journals

Cited by 2 publications

(1 citation statement)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [11] it was proved that the overdetermined problem corresponding to the stationarity conditions for the torsional rigidity and for the first Dirichlet eigenvalue of the Laplacian, under an area or a perimeter constraint, characterizes the equilateral triangle among all triangles. We also mention the recent paper [20] for a related result, where equilateral triangles are characterized in terms of the position of the maximum point of the associated potential.…”

Section: Introductionmentioning

confidence: 99%

Riesz-type inequalities and overdetermined problems for triangles and quadrilaterals

Bonacini,

Cristoferi,

Topaloglu

2021

Preprint

View full text Add to dashboard Cite

We consider Riesz-type nonlocal interaction energies over convex polygons. We prove the analog of the Riesz inequality in this discrete setting for triangles and quadrilaterals, and obtain that among all N -gons with fixed area, the nonlocal energy is maximized by a regular polygon, for N = 3, 4. Further we derive necessary first-order stationarity conditions for a polygon with respect to a restricted class of variations, which will then be used to characterize regular N -gons, for N = 3, 4, as solutions to an overdetermined free boundary problem.

show abstract

Section: Introductionmentioning

confidence: 99%