Convex Shapes and Harmonic Caps

Laura DeMarco; Kathryn Lindsey

doi:10.1007/s40598-016-0061-7

Convex Shapes and Harmonic Caps

Laura DeMarco^*, Kathryn Lindsey

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Any planar shape P⊂ C can be embedded isometrically as part of the boundary surface S of a convex subset of R³ such that ∂P supports the positive curvature of S. The complement Q= S\ P is the associated cap. We study the cap construction when the curvature is harmonic measure on the boundary of (C^ \ P, ∞). Of particular interest is the case when P is a filled polynomial Julia set and the curvature is proportional to the measure of maximal entropy.

Original language	English (US)
Pages (from-to)	97-117
Number of pages	21
Journal	Arnold Mathematical Journal
Volume	3
Issue number	1
DOIs	https://doi.org/10.1007/s40598-016-0061-7
State	Published - Apr 1 2017

Keywords

Convex shape
Curvature
Harmonic measure
Julia set
Polyhedra

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.1007/s40598-016-0061-7

Cite this

@article{2b51221fdd7a42ddb28325871d0331f3,

title = "Convex Shapes and Harmonic Caps",

abstract = "Any planar shape P⊂ C can be embedded isometrically as part of the boundary surface S of a convex subset of R3 such that ∂P supports the positive curvature of S. The complement Q= S\ P is the associated cap. We study the cap construction when the curvature is harmonic measure on the boundary of (C^ \ P, ∞). Of particular interest is the case when P is a filled polynomial Julia set and the curvature is proportional to the measure of maximal entropy.",

keywords = "Convex shape, Curvature, Harmonic measure, Julia set, Polyhedra",

author = "Laura DeMarco and Kathryn Lindsey",

note = "Funding Information: Our research was supported by the National Science Foundation and the Simons Foundation. Publisher Copyright: {\textcopyright} 2017, Institute for Mathematical Sciences (IMS), Stony Brook University, NY.",

year = "2017",

month = apr,

day = "1",

doi = "10.1007/s40598-016-0061-7",

language = "English (US)",

volume = "3",

pages = "97--117",

journal = "Arnold Mathematical Journal",

issn = "2199-6792",

publisher = "Springer International Publishing AG",

number = "1",

}

TY - JOUR

T1 - Convex Shapes and Harmonic Caps

AU - DeMarco, Laura

AU - Lindsey, Kathryn

N1 - Funding Information: Our research was supported by the National Science Foundation and the Simons Foundation. Publisher Copyright: © 2017, Institute for Mathematical Sciences (IMS), Stony Brook University, NY.

PY - 2017/4/1

Y1 - 2017/4/1

N2 - Any planar shape P⊂ C can be embedded isometrically as part of the boundary surface S of a convex subset of R3 such that ∂P supports the positive curvature of S. The complement Q= S\ P is the associated cap. We study the cap construction when the curvature is harmonic measure on the boundary of (C^ \ P, ∞). Of particular interest is the case when P is a filled polynomial Julia set and the curvature is proportional to the measure of maximal entropy.

AB - Any planar shape P⊂ C can be embedded isometrically as part of the boundary surface S of a convex subset of R3 such that ∂P supports the positive curvature of S. The complement Q= S\ P is the associated cap. We study the cap construction when the curvature is harmonic measure on the boundary of (C^ \ P, ∞). Of particular interest is the case when P is a filled polynomial Julia set and the curvature is proportional to the measure of maximal entropy.

KW - Convex shape

KW - Curvature

KW - Harmonic measure

KW - Julia set

KW - Polyhedra

UR - http://www.scopus.com/inward/record.url?scp=85034653876&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85034653876&partnerID=8YFLogxK

U2 - 10.1007/s40598-016-0061-7

DO - 10.1007/s40598-016-0061-7

M3 - Article

AN - SCOPUS:85034653876

SN - 2199-6792

VL - 3

SP - 97

EP - 117

JO - Arnold Mathematical Journal

JF - Arnold Mathematical Journal

IS - 1

ER -

Convex Shapes and Harmonic Caps

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this