Differentiation Properties of the Perimeter to Area Ratio for Finitely Many Overlapped Unit Squares

@ARTICLE{ jaa:article,
AUTHOR = {Humke, Paul and Marcott, Cameron and Mellem, Bjorn and Stiegler, Cole},
TITLE = {Differentiation Properties of the Perimeter to Area Ratio for Finitely Many Overlapped Unit Squares},
JOURNAL = {},
YEAR = {},
VOLUME = {},
NUMBER = {},
PAGES = {},
NOTE = {submitted for publication}
	}

@ARTICLE{ gyenes:article,
AUTHOR = {Gyenes, Zolt\'{a}n},
TITLE = {The Ratio of the Perimeter and the Area of Unions of Copies of a Fixed Set},
JOURNAL = {Discrete and Computational Geometry},
YEAR = {2011},
VOLUME = {45},
NUMBER = {3},
PAGES = {400-409},
NOTE = {\href{www.springerlink.com/content/h4706266q6rr4m37/fulltext.pdf}{www.springerlink.com/content/h4706266q6rr4m37/fulltext.pdf}}
	}

@ARTICLE{ keleti:covering_property,
AUTHOR = {Keleti, Tam\'{a}s},
TITLE = {A Covering Property of Some Classes of Sets in {${\mathbb{R}^n}$}},
JOURNAL = {Acta Universitatis Carolinae-Mathematica et Physica},
YEAR = {1998},
VOLUME = {39},
NUMBER = {1-2},
PAGES = {111-118}},
EPRINT = {\href{dml.cz/bitstream/handle/10338.dmlcz/702048/ActaCarolinae_039-1998-1_8.pdf}{dml.cz/bitstream/handle/10338.dmlcz/702048/ActaCarolinae_039-1998-1_8.pdf}}}

@misc{ schweitzer:1998,
key = {Schweitzer},
author = {},
title = {Schweitzer Mikl\'{o}s Matematikai Eml\'{e}kverseny},
year = {1998},
note = {\href{www.math.u-szeged.hu/~mmaroti/schweitzer/schweitzer-1998.pdf}{www.math.u-szeged.hu/ $\sim$mmaroti/schweitzer/schweitzer-1998.pdf}}
	}


@misc{ gyenes:thesis,
author = {Gyenes, Zolt\'an},
school = {E\"otv\"os Lor\'and University},
title = {The ratio of the surface-area and volume of finite union of copies of a fixed set in $\mathbb{R}^n$},
year = {2005},
note = {\href{http://www.cs.elte.hu/~dom/z.pdf}{http://www.cs.elte.hu/$\sim$dom/z.pdf}}
	}
	
	
@incollection{Cheng:2003:APD:865449.865457,
 author = {Cheng, Ho-Lun and Edelsbrunner, Herbert},
 title = {Area and perimeter derivatives of a union of disks},
 booktitle = {Computer Science in Perspective},
 editor = {Klein, Rolf and Six, Hans-Werner and Wegner, Lutz},
 year = {2003},
 isbn = {3-540-00579-X},
 pages = {88--97},
 numpages = {10},
 url = {http://dl.acm.org/citation.cfm?id=865449.865457},
 acmid = {865457},
 publisher = {Springer-Verlag New York, Inc.},
 address = {New York, NY, USA},
 keywords = {Voronoi diagram, alpha complex, area, derivative, disks, perimeter},
} 

@ARTICLE{Bezdek01pushingdisks,
    author = {K‡roly Bezdek and Robert Connelly},
    title = {Pushing disks apart Ñ the KneserÐPoulsen conjecture in the plane},
    journal = {J. REINE ANGEW. MATH},
    year = {2001},
    volume = {53},
    pages = {221--236}
}

@ARTICLE{Bollobas,
    author = {B\'ela Bollob\'as},
    title = {Area of the Union of Disks},
    journal = {Elem. Math.},
    year = {1968},
    volume = {23},
    pages = {60-61}
}