Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.10976

Symmetric products of absolute Lipschitz retracts

Leonid V. Kovalev
View original source ↗Read source document ↗Export metadata ↓

Abstract

We prove that the Qth symmetric product of an absolute $λ$-Lipschitz retract, equipped with the bottleneck matching metric, is an absolute $(3Q-2)λ$-Lipschitz retract. This answers a question of De Pauw about the target spaces of Almgren's Q-valued maps. The main tool is a reconstruction theorem for bounded products of metric stars with finitely many rays, modulo a finite permutation group: these quotients are absolute 3-Lipschitz retracts, independently of the group and the number of coordinates.

Explore related subjects

math.MG

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Leonid V. Kovalev. 2026-10-07. Symmetric products of absolute Lipschitz retracts. https://arxiv.org/abs/2610.10976

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Limits of mapping packages and tangents of Sobolev maps

We show the existence of ultralimits of sequences of Hajlasz-Sobolev mappings $f_i:X_i\to Y_i$ when $X_i$ converges to a limit space in the pointed measured Gromov (pmG) sense, partially extending recent results in [T. Ikonen and S. Wenger, (2026), arXiv:2603.05246]. We moreover demonstrate that the mappings pmG-converge to the ultralimit in a suitable sense, and obtain Arzela-Ascoli theorems in the context of pmG-convergence. As an application, we establish a version of Preiss's phenomenon for Hajlasz-Sobolev maps $f:(X,μ)\to V$ into arbitrary Banach spaces. Besides extending it to maps into infinite dimensional targets, our result generalizes existing versions of Preiss's phenomenon [G. C. David, Geom. Funct. Anal., 25 (2015)], [N. Gigli, A. Mondino, and T. Rajala, J. Reine Angew. Math., 705 (2015)] by establishing it for pointed measured Gromov-Hausdorff tangents without a doubling assumption.

math.MG↗
arXiv2026

Chasing rotational symmetry in the spectre tiling

We identify the rotational symmetry centers in the spectre tiling. We find that both 2-fold and 3-fold symmetry centers are coexisting, with two different types of 3-fold centers. Local and global symmetry operations are distinguished, and characterized in terms of substitution systems. We introduce a decomposition of the spectre tiling in terms of three metatiles named diabolo, 2-arms and 3-arms, valid at any substitution level. We propose geometrical constructions for generating patches of the spectre tiling with 2-fold and 3-fold global rotational symmetry.

math.MG↗
arXiv2026

Sharp Minimax Gram-Determinant Asymptotics for Labelled Unit Decompositions of the Identity and Recent Developments on Makai's Conjecture

We show that González Merino and Schymura's Conjecture 4.8, a sufficient condition for Makai's reverse isodiametric conjecture, fails in all sufficiently large dimensions. Its three-dimensional case follows from Aliev's proof. Pełczyński and Szarek's construction for enclosing parallelepipeds implies this failure. Using random frames, we also determine the sharp exponential determinant guarantee for every fixed ratio greater than one between the number of vectors and the dimension.

math.MG↗