On the average number of normals through points of a convex body

G. Domokos, Zsolt Lángi

Research output: Contribution to journalArticle

Abstract

In 1944, Santaló asked about the average number of normals through a point of a given convex body. Since then, numerous results appeared in the literature about this problem. The aim of this paper is to add to this list some new, recent developments. We point out connections of the problem to static equilibria of rigid bodies as well as to geometric partial differential equations of surface evolution.

Original languageEnglish
Pages (from-to)457-476
Number of pages20
JournalStudia Scientiarum Mathematicarum Hungarica
Volume52
Issue number4
DOIs
Publication statusPublished - Dec 1 2015

Fingerprint

Convex Body
Rigid Body
Partial differential equation

Keywords

  • Constant width bodies
  • Convex bodies
  • Diameter
  • Eikonal equation
  • Inner normals
  • Static equilibrium

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

On the average number of normals through points of a convex body. / Domokos, G.; Lángi, Zsolt.

In: Studia Scientiarum Mathematicarum Hungarica, Vol. 52, No. 4, 01.12.2015, p. 457-476.

Research output: Contribution to journalArticle

@article{4dc759c954b845539efbc96d19a37063,
title = "On the average number of normals through points of a convex body",
abstract = "In 1944, Santal{\'o} asked about the average number of normals through a point of a given convex body. Since then, numerous results appeared in the literature about this problem. The aim of this paper is to add to this list some new, recent developments. We point out connections of the problem to static equilibria of rigid bodies as well as to geometric partial differential equations of surface evolution.",
keywords = "Constant width bodies, Convex bodies, Diameter, Eikonal equation, Inner normals, Static equilibrium",
author = "G. Domokos and Zsolt L{\'a}ngi",
year = "2015",
month = "12",
day = "1",
doi = "10.1556/012.2015.52.4.1320",
language = "English",
volume = "52",
pages = "457--476",
journal = "Studia Scientiarum Mathematicarum Hungarica",
issn = "0081-6906",
publisher = "Akademiai Kiado",
number = "4",

}

TY - JOUR

T1 - On the average number of normals through points of a convex body

AU - Domokos, G.

AU - Lángi, Zsolt

PY - 2015/12/1

Y1 - 2015/12/1

N2 - In 1944, Santaló asked about the average number of normals through a point of a given convex body. Since then, numerous results appeared in the literature about this problem. The aim of this paper is to add to this list some new, recent developments. We point out connections of the problem to static equilibria of rigid bodies as well as to geometric partial differential equations of surface evolution.

AB - In 1944, Santaló asked about the average number of normals through a point of a given convex body. Since then, numerous results appeared in the literature about this problem. The aim of this paper is to add to this list some new, recent developments. We point out connections of the problem to static equilibria of rigid bodies as well as to geometric partial differential equations of surface evolution.

KW - Constant width bodies

KW - Convex bodies

KW - Diameter

KW - Eikonal equation

KW - Inner normals

KW - Static equilibrium

UR - http://www.scopus.com/inward/record.url?scp=84951121772&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84951121772&partnerID=8YFLogxK

U2 - 10.1556/012.2015.52.4.1320

DO - 10.1556/012.2015.52.4.1320

M3 - Article

VL - 52

SP - 457

EP - 476

JO - Studia Scientiarum Mathematicarum Hungarica

JF - Studia Scientiarum Mathematicarum Hungarica

SN - 0081-6906

IS - 4

ER -