An Integration Approach To The Toeplitz Square Peg Problem

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forumofmathematics sigma 2017 vol 5 e30 63pages 1 doi 10 1017 fms 2017 23 anintegrationapproachtothe toeplitzsquarepegproblem terencetao ucladepartmentofmathematics losangeles ca90095 1555 usa email tao math ucla edu received 22 november ...

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...Forumofmathematics sigma vol e pages doi fms anintegrationapproachtothe toeplitzsquarepegproblem terencetao ucladepartmentofmathematics losangeles ca usa email tao math ucla edu received november accepted september abstract the square peg problem or inscribed of toeplitz asks if every simple closed curve in plane inscribes a nondegenerate sense that all four vertices lie on by variety arguments homological nature it is known answer to this question positive sufciently regular regularity hypotheses are needed rule out possibility arbitrarily small squares almost onthecurve becauseofthis theseargumentsdonotappeartoberobustenoughtohandlearbitrarily rough curves paper we augment approach introducing certain integrals associated able give answers some new cases for instance union two lipschitz graphs f g r agree at endpoints and whose constants strictly less than one also present simpler variants which seem particularly amenable integration includingaperiodicversionoftheproblemthatisnotsubj...

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Posted on: 29 Jan 2023 | 4 years ago
Tag: download pdf, integration, approach, toeplitz, square, problem,
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