Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Thursday, November 19, 2009, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Marek Sulovský

A few words about continuous motion in geometry

ontinuous motion is proof method in geometry used to prove certain properties of point sets by transforming some "simple" point set (where we know what happens) to an arbitrary point set. The key ingredient to the proof is then controlling the "relevant changes" during this transformation and proving, that the desired property is preserved during these changes.

This technique was successfully used to prove a so called crossing identity for k-edges in the plane [AAHSW'98], which we will use for its illustration. After that, we will state and explain result of similar nature, which we obtained ([SW'*]) by continuous motion for point configurations on a sphere and in R^3.

References:
AAHSW'98: Anrzejak, Aronov, Har-Peled, Seidel, Welzl '98: Results on k-Sets and j-Facets via Continuous Motion (SCG'98)
SW'*: Sulovsky, Wagner: k-Sets and Convex Continuous Motion in R^3 (unpublished)

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