Fetching the paper…
Reading the bibliography…
We prove that any convex body in the plane can be partitioned into $m$ convex parts of equal areas and perimeters for any integer $m\ge 2$; this result was previously known for prime powers $m=p^k$.
On the continuous function defined on a sphere
H. Yamabe and Z. Yujobo · 1950
Earlier work this paper cites.
Introduction to Piecewise-Linear Topology
C. P. Rourke and B. J. Sanderson · 1972
Earlier work this paper cites.
A Geometric Approach to Homology Theory
S. Buoncristiano, C. P. Rourke, and B. J. Sanderson · 1976
Earlier work this paper cites.
Braid group cohomologies and algorithm complexity
V. A. Vassiliev · 1988
Earlier work this paper cites.
On the representation theory associated to the cohomology of configuration spaces
F. R. Cohen and L. R. Taylor · 1993
Earlier work this paper cites.
Minkowski-type theorems and least-square clustering
F. Aurenhammer, F. Hoffmann, and B. Aronov · 1998
Earlier work this paper cites.
Generalizing ham sandwich cuts to equitable subdivisions
S. Bespamyatnikh, D. Kirkpatrick, and J. Snoeyink · 2000
Earlier work this paper cites.
Isoperimetry of waists and concentration of maps
M. Gromov · 2003
Cited alongside, same era.
Using the Borsuk-Ulam theorem: Lectures on topological methods in combinatorics and geometry
J. Matoušek · 2003
Cited alongside, same era.
Elements of combinatorial and differential topology
V. V. Prasolov · 2006
Cited alongside, same era.
Convex and Discrete Geometry
P. M. Gruber · 2007
Cited alongside, same era.
‘Fair’ partitions of polygons – an introduction
R. Nandakumar and N. Ramana Rao · 2008
Cited alongside, same era.
S. Avvakumov and R. Karasev · 2009
Equipartitioning by a convex 3 3 -fan
I. Bárány, P. Blagojević, and A. Szűcs · 2010
Later among the works it cites.
Balanced convex partitions of measures in ℝ d \mathbb{R}^{d}
P. Soberón · 2012
Later among the works it cites.
Convex equipartitions via equivariant obstruction theory
P. Blagojević and G. Ziegler · 2014
Later among the works it cites.
Convex equipartitions: the spicy chicken theorem
R. Karasev, A. Hubard, and B. Aronov · 2014
Later among the works it cites.
Convex geometry and waist inequalities
B. Klartag · 2017
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Cited alongside, same era.
The genus and the category of configuration spaces
R. Karasev · 2009
Cited alongside, same era.
Théorie des fonctions numériques simplement périodiques. Part II
E. Lucas
Cited in the paper.
P. Blagojević and N. Sadovek · 2023
Closest in time.