The Lip-lip equality is stable under blow-up

Abstract

We show that at generic points blow-ups/tangents of differentiability spaces are still differentiability spaces; this implies that an analytic condition introduced by Keith as an inequality (and later proved to actually be an equality) passes to tangents. As an application, we characterize the $p$-weak gradient on iterated blow-ups of differentiability spaces.

minor corrections: change of normalization of the measures; The final version will appear in Calc. Var. PDE

References in corpus (4)

• Derivations and Alberti representations
• Differentiating maps into L^1 and the geometry of BV functions
• Differentiable structures on metric measure spaces: A Primer
• Metric spaces with unique tangents

Cited by in corpus (5)

• Derivations and Alberti representations
• Differentiability and Poincaré-type inequalities in metric measure spaces
• An example of a differentiability space which is PI-unrectifiable
• Unrectifiable normal currents in Euclidean spaces
• Lipschitz functions with prescribed blowups at many points