An integration approach to the Toeplitz square peg problem | Vidéo | Carmin.tv

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An integration approach to the Toeplitz square peg problem

Appears in collections : Harmonic analysis and geometric measure theory / Analyse harmonique et théorie géométrique de la mesure, The Fields Medallists, Fields medallists - 2006

The Toeplitz square peg problem asks if every simple closed curve in the plane inscribes a square. This is known for sufficiently regular curves (e.g. polygons), but is open in general. We show that the answer is affirmative if the curve consists of two Lipschitz graphs of constant less than 1 using an integration by parts technique, and give some related problems which look more tractable.

Information about the video

Date of recording 04/10/2017
Date of publication 06/10/2017
Institution CIRM
Licence CC BY NC ND
Language English
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19226703
Cite this video Tao, Terence (04/10/2017). An integration approach to the Toeplitz square peg problem. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19226703
URL https://dx.doi.org/10.24350/CIRM.V.19226703

Domain(s)

Bibliography

Matschke, B. (2014). A survey on the square peg problem, Notices of the American Mathematical Society, 61(4), 346-352 - http://dx.doi.org/10.1090/noti1100
Tao, T. (2017). An integration approach to the Toeplitz square peg problem. <arXiv:1611.07441> - https://arxiv.org/abs/1611.07441
Toeplitz, 0. (1911). Ueber einige Aufgaben der Analysis situs. In Verhandlungen der schweizerischen naturforschenden Gesellschaft. 94. Jahresversammlung vom 30. Juli bis 2. August 1911 in Solothurn (p. 197). Aarau: H. R. Sauerländer - https://archive.org/stream/verhandlungender1911schw

MSC codes

55N45 Products and intersections

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