An Isodiametric Problem with Additional Constraints in Euclidean space R³

2015/03/11 by Yi Yang, Yang, Yi
Engineering · Mathematics · #42A38 #52A40 #Differential Equations and Boundary Problems #Dynamical Systems (math.DS) #Elasticity and Wave Propagation #FOS: Mathematics #Material Science and Thermodynamics

paper · pdf · doi:10.48550/arxiv.1503.03364

openalex publication_date 2015/03/11 · openalex created_date 2020/05/13 · openalex updated_date 2026/07/28

Abstract

Let C_θ be a circular cone in Euclidean space ℝ³,which apex is the origin and apex angle of the cone is θ∈ (π/3, π). Let M_θ be the class of compact convex domains in Euclidean space ℝ³, which have diameter one, contains the origin and are included in C_θ. In this paper, we show that there is a unique compact convex domain with maximal volume and also we determine the shape of the above domain.

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