Dimension reduction in metric geometry represents a finite collection of points in a space of smaller dimension while controlling their distances. The permitted error is measured by metric embedding distortion. The representing function need not be a linear transformation.
For 
,
integer 
, and 
, let 
be the least coordinate dimension
in which every 
-point subset of any real Lp-space
can be represented with metric embedding
distortion at most 
. The target is 
, with norm 
.
-Isometric Dimension Reduction for Incompressible Subsets
of 
."
Disc. Comput. Geom. 71, 160-176, 2024.