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.
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Acknowledgments
This work would have not been possible without the many conversations that I had with David Preiss, who generously invited me to visit the University of Warwick; I also wish to thank the people in the analysis group, in particular Daniel Seco, for the hospitality I received. I also thank the anonymous referee for reading the manuscript very carefully and for pointing out an issue with the way measures were normalized in the first version of the preprint.
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Communicated by L. Ambrosio.
The author was supported by the “ETH Zurich Postdoctoral Fellowship Program and the Marie Curie Actions for People COFUND Program” and the European Research Council Grant no. 291497.
