Timeline for Can iterative application of ham sandwich cuts form streamlines of an ODE?
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Sep 10, 2021 at 18:46 | comment | added | user483904 | The ODE that I need is that $\dot{X} = f(X)$, where $f:\mathbb{R}^d\rightarrow \mathbb{R}^d$ is Lipschitz continuous. But I am totally fine with piecewise Lipschitz continuous. | |
| Sep 10, 2021 at 18:40 | comment | added | user483904 | I want to find those cuts first (i.e., apply ham sandwich theorem, or some other results...), and then prove that these cuts/curves are streamlines of an ODE (i.e., prove the existence of an ODE $\dot{X} = f(X)$ with $f$ being continuous such that its streamlines are exactly the cuts we find by iteratively applying ham sandwich theorem). My intuition is that I hope those cuts do not interact in a strange way (e.g., totally horizontal and vertical cuts intersecting with each other in a strange way) by imposing regularity assumption on probability measures, but I don't know where to get started. | |
| Sep 10, 2021 at 17:07 | comment | added | Ben McKay | If you just use straight lines to make your cuts, they are the solutions of an ODE: free particles in space. Do you want to pick the ODE first, and then make the cuts? Can you say more maybe about what sort of ODE you want? If the measures both lie entirely along a streamline, and the streamlines foliate (1st order ODE), you won't be able to do this | |
| Sep 10, 2021 at 16:28 | history | asked | user483904 | CC BY-SA 4.0 |