Year: 2026
Type: article
Abstract: We prove that an infinitesimally Hilbertian C D ( 0 , N ) CD(0,N) space containing a line splits as the product of R \mathbb {R} and an infinitesimally Hilbertian C D ( 0 , N − 1 ) CD(0,N-1) space. By ‘infinitesimally Hilbertian’ we mean that the Sobolev space W 1 , 2 ( X , d , m ) W^{1,2}(X,\mathsf {d},\mathfrak {m}) , which in general is a Banach space, is an Hilbert space. When coupled with a curvature-dimension bound, this condition is known to be stable with respect to measured Gromov-Hausdorff convergence.
DOI: 10.1090/memo/1609
Author: Nicola Gigli
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7127596762