The Reeb Graph Edit Distance is Universal
Sign Up to like & getrecommendations! Published in 2021 at "Foundations of Computational Mathematics"
DOI: 10.1007/s10208-020-09488-3
Abstract: We consider the setting of Reeb graphs of piecewise linear functions and study distances between them that are stable, meaning that functions which are similar in the supremum norm ought to have similar Reeb graphs.… read more here.
Keywords: distance; reeb; edit distance; reeb graphs ... See more keywords
Using Foliation Leaves To Extract Reeb Graphs On Surfaces
Sign Up to like & getrecommendations! Published in 2022 at "IEEE Transactions on Visualization and Computer Graphics"
DOI: 10.1109/tvcg.2022.3141764
Abstract: For Reeb graph extraction on surfaces, existing methods always use the isolines of a function defined on the surface to detect the surface components and the neighboring relationships between them. Since such detection is unstable,… read more here.
Keywords: using foliation; reeb; surface; reeb graphs ... See more keywords
Rigid constellations of closed Reeb orbits
Sign Up to like & getrecommendations! Published in 2017 at "Compositio Mathematica"
DOI: 10.1112/s0010437x17007448
Abstract: We use Hamiltonian Floer theory to recover and generalize a classic rigidity theorem of Ekeland and Lasry. That theorem can be rephrased as an assertion about the existence of multiple closed Reeb orbits for certain… read more here.
Keywords: rigid constellations; contact forms; reeb; closed reeb ... See more keywords