MathDB3 problems
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The non-geodesicity conjecture for metric spaces of Reeb graphs
Non-geodesicity conjecture. The space of isomorphism classes of Reeb graphs with metric is not a geodesic space.
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The contour-tree geodesic conjecture for interleaving distance
Contour-tree geodesic conjecture. When a Reeb graph has no loop, the geodesic property holds.
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Carrière–Oudot's local equivalence conjecture for broader metric spaces
Carrière and Oudot's work concerns metric spaces equipped with metrics analogous to those studied for Reeb graphs, including a computable metric and an intrinsic metric. Carrière–O…