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The new estimator is shown to be consistent and its convergence rates in terms of the Hausdorff distance are provided. All consistency results are established uniformly on the level of the set and for any Riemannian manifold M satisfying mild assumptions. The applicability of the procedure is shown by some illustrative examples.<\/jats:p>","DOI":"10.1214\/26-aos2648","type":"journal-article","created":{"date-parts":[[2026,10,2]],"date-time":"2026-10-02T12:50:45Z","timestamp":1790945445000},"page":"2379-2405","source":"Crossref","is-referenced-by-count":0,"title":["Granulometric smoothing on manifolds"],"prefix":"10.1214","volume":"54","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2655-1073","authenticated-orcid":false,"given":"Diego","family":"Bol\u00f3n","sequence":"first","affiliation":[{"name":"ECARES and Department of Mathematics, Universit\u00e9 libre de Bruxelles"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3907-8951","authenticated-orcid":false,"given":"Rosa M.","family":"Crujeiras","sequence":"additional","affiliation":[{"name":"Galician Center for Mathematical Research and Technology, CITMAga, Universidade de Santiago de Compostela"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9603-5931","authenticated-orcid":false,"given":"Alberto","family":"Rodriguez-Casal","sequence":"additional","affiliation":[{"name":"Galician Center for Mathematical Research and Technology, CITMAga, Universidade de Santiago de Compostela"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"108","reference":[{"key":"9","unstructured":"<small>Billingsley, P.<\/small> (1995). <i>Probability and Measure<\/i>, 3rd ed. <i>Wiley Series in Probability and Mathematical Statistics<\/i>. 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