### Lower and upper bounds for the waists of different spaces

#### Abstract

#### Keywords

#### References

A. Akopyan and R. Karasev, A tight estimate for the waist of the ball, Bull. Lond. Math. Soc. 49 (2017), no. 4, 690–693, http://arxiv.org/abs/1608.06279.

A. Akopyan, R. Karasev and F. Petrov, Bang’s problem and symplectic invariants (2014), http://arxiv.org/abs/1404.0871.

A. Akopyan, R. Karasev and A. Volovikov, Borsuk–Ulam type theorems for metric spaces (2012), http://arxiv.org/abs/1209.1249.

F.J. Almgren, The theory of varifolds: a variational calculus in the large for the k-dimensional area integrand, 1965.

I. Bárány and L Lovász, Borsuk’s theorem and the number of facets of centrally symmetric polytopes, Acta Math. Hungar. 40 (1982), 323–329.

F. Barthe and B. Maurey, Some remarks on isoperimetry of Gaussian type, Ann. Inst. Henri Poincaré Probab. Stat. 36 (2000), 419–434.

G. David and S.W. Semmes, Analysis of and on Uniformly Rectifiable Sets, Amer. Math. Soc., 1993.

H. Federer, Geometric Measure Theory, Springer Verlag, 1969.

M. Gromov, Filling Riemannian manifolds, J. Differential Geom. 18 (1983), 1–147.

M. Gromov, Isoperimetry of waists and concentration of maps, Geom. Funct. Anal. 13 (2003), 178–215.

M. Gromov, Dimension, Non Linear Spectra and Width, Geometric Aspects of Functional Analysis, Lecture Notes in Mathematics, Vol. 1317, Springer, 2006.

M. Gromov, Singularities, expanders and topology of maps. Part 2. From combinatorics to topology via algebraic isoperimetry, Geom. Funct. Anal. 20 (2010), 416–526.

L. Guth, The width-volume inequality (2006), https://arxiv.org/abs/math/0609569.

L. Guth, Minimax problems related to cup powers and Steenrod squares, Geom. Funct. Anal. 18 (2008), 1917–1987, https://arxiv.org/abs/math/0702066.

L. Guth, Metaphors in systolic geometry (2010), https://arxiv.org/abs/1003.4247.

L. Guth, The waist inequality in Gromov’s work, The Abel Prize 2008–2012, Springer, 2014, 139–234, http://dx.doi.org/10.1007/978-3-642-39449-2 11.

H. Hadwiger, Gitterperiodische Punktmengen und Isoperimetrie, Monatsh. Math. 76 (1972), 410–418.

R. Karasev, A topological central point theorem, Topology Appl. 159 (2012), 864–868.

R. Karasev, An analogue of Gromov’s waist theorem for coloring the cube, Discrete Comput. Geom. 49 (2013), 444–453, http://arxiv.org/abs/1109.1078.

R. Karasev and A. Volovikov, Waist of the sphere for maps to manifolds, Topology Appl. 160 (2013), 1592–1602, http://arxiv.org/abs/1102.0647.

B. Klartag, Convex geometry and waist inequalities, Geom. Funct. Anal. 27 (2017), 130–164, http://arxiv.org/abs/1608.04121.

B. Klartag, Eldan’s stochastic localization and tubular neignbourhoods of complexanalytic sets, J. Geom. Anal. 28 (2017), no. 3, 2008–2027, http://arxiv.org/abs/1702. 02315.

A. Koldobsky, Fourier Analysis in Convex Geometry, Amer. Math. Soc., 2005.

R. Latala and J.O. Wojtaszczyk, On the infimum convolution inequality, Studia Math. 189 (2008), 147–187.

Y. Liokumovich, F.C. Marquez and A. Neves, Weyl law for the volume spectrum (2016), https://arxiv.org/abs/1607.08721v1.

M. Matdinov, Size of components of a cube coloring, Discrete Comput. Geom 50 (2013), 185–193, http://arxiv.org/abs/1111.3911.

J. Matoušek and A Přı́vĕtivý, Large monochromatic components in two-colored grids, SIAM J. Discrete Math. 22 (2008), 295–311.

Y. Memarian, On Gromov’s waist of the sphere theorem, J. Topology Anal. 3 (2011), 7–36, http://arxiv.org/abs/0911.3972.

F. Morgan, Geometric Measure Theory. A Beginner’s Guide, Elsevier, 2009.

M. Ritoré and A. Ros, Stable constant mean curvature tori and the isoperimetric problem in three space forms, Comment. Math. Helv. 67 (1992), 293–305.

A. Ros, The isoperimetric problem (2001), http://www.ugr.es/ aros/isoper.pdf.

### Refbacks

- There are currently no refbacks.