{"ID":23629741,"CreatedAt":"2026-09-18T07:04:54.147703138Z","UpdatedAt":"2026-09-18T07:04:54.147703138Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2609.20706","arxiv_id":"2609.20706","title":"Hölder Selections under Stieltjes Clocks: Uniform Disconnectedness and Jump Dominance","abstract":"It is known that, for ordinary Hölder multifunctions with 0 \u003c α \u003c 1, Hölder regularity alone does not guarantee the existence of a Hölder selection, and in general even a continuous selection may fail to exist. We ask how this situation changes when the parameter is measured through a Stieltjes clock. For 0 \u003c α \u003c 1, we characterize the clocks for which every compact-valued g-Hölder multifunction admits a g-Hölder selection. The determining condition is uniform disconnectedness of the clock image Im(g). For left-continuous and nondecreasing clocks, this condition is equivalent to uniform jump dominance: every positive clock increment contains a jump carrying a fixed positive fraction of that increment. Under this condition, a selection can be chosen through any prescribed point of the graph, with explicit control of its Hölder regularity. Conversely, when the condition fails, there exists a compact-valued g-Hölder multifunction with no g-Hölder selection. The results show that the selection property is governed not simply by the presence of jumps, but by how their sizes are distributed across scales.","short_abstract":"It is known that, for ordinary Hölder multifunctions with 0 \u003c α \u003c 1, Hölder regularity alone does not guarantee the existence of a Hölder selection, and in general even a continuous selection may fail to exist. We ask how this situation changes when the parameter is measured through a Stieltjes clock. For 0 \u003c α \u003c 1, we...","url_abs":"https://arxiv.org/abs/2609.20706","url_pdf":"https://arxiv.org/pdf/2609.20706v1","authors":"[\"Serkan İlter\",\"Hülya Duru\",\"Arkady Kitover\",\"Mehmet Orhon\"]","published":"2026-09-17T17:05:35Z","proceeding":"math.GN","tasks":"[\"math.GN\",\"math.MG\"]","methods":"[]","has_code":false}