2013
DOI: 10.1007/978-3-642-39449-2_11
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A Few Snapshots from the Work of Mikhail Gromov

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Cited by 5 publications
(8 citation statements)
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References 130 publications
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“…If we allowed the constant ε k,n to depend on Y then this sort of result would follow from the case Y = R k , just because any k-dimensional Y can be mapped to R k with bounded multiplicity. A similar theorem was considered by Gromov in [8, Appendix 2, B2'], see also [15,Section 7]; we report our similar proof since some readers might profit from the connection to colorings of the cube.…”
supporting
confidence: 64%
See 1 more Smart Citation
“…If we allowed the constant ε k,n to depend on Y then this sort of result would follow from the case Y = R k , just because any k-dimensional Y can be mapped to R k with bounded multiplicity. A similar theorem was considered by Gromov in [8, Appendix 2, B2'], see also [15,Section 7]; we report our similar proof since some readers might profit from the connection to colorings of the cube.…”
supporting
confidence: 64%
“…For much more information on waist inequalities see Gromov's papers, and Guth's essay[15] and papers.…”
mentioning
confidence: 99%
“…For the latter value, we can introduce the following notation: For example, for Proposition 2.8 implies b(R n ) = ∞, n ≥ 2. Our definition of the Reeb width b(X) closely resembles that of Urysohn width (5). Indeed, when appropriate, one can consider the Reeb graph R f as Y 1 and the Reeb quotient map as ϕ in (5).…”
Section: Diameters Of Contours On Disks and On Riemannian Manifoldsmentioning
confidence: 99%
“…We assume that M is a compact connected piecewise-linear (PL) d-dimensional manifold, without boundary. That is, we assume that M admits a triangulation 4 T with the property that the link of every nonempty simplex τ of T is a PL sphere of dimension d − 1 − dim(τ ); throughout this paper, we only consider triangulations of M that have this property.…”
Section: Assumptions On Mmentioning
confidence: 99%
“…In the special case where X is the n-dimensional simplex ∆ n (or its d-dimensional skeleton), determining the optimal overlap constant for maps ∆ n → Ê d is a classical problem in discrete geometry, also known as the point selection problem [2,1] and originally only considered for affine maps. Apart from the generalization from affine to arbitrary continuous maps, Gromov's proof also led to improved estimates for the point selection problem, and a number of papers have appeared with expositions and simplified proofs of Gromov's result in this special case X = ∆ n , see [9,13] and [4,Sec. 7.8].…”
Section: Introductionmentioning
confidence: 99%