Isoperimetric inequalities for inner parallel curves

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F24%3A00600555" target="_blank" >RIV/61389005:_____/24:00600555 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.4171/JST/534" target="_blank" >https://doi.org/10.4171/JST/534</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4171/JST/534" target="_blank" >10.4171/JST/534</a>

Result language
angličtina
Original language name
Isoperimetric inequalities for inner parallel curves
Original language description
We prove weighted isoperimetric inequalities for smooth, bounded, and simplyconnected domains. More precisely, we show that the moment of inertia of inner parallel curves for domains with fixed perimeter attains its maximum for a disk. This inequality, which was previously only known for convex domains, allows us to extend an isoperimetric inequality for the magnetic Robin Laplacian to non-convex centrally symmetric domains. Furthermore, we extend our isoperimetric inequality for moments of inertia, which are second moments, to p-th moments for all p smaller than or equal to two. We also show that the disk is a strict local maximiser in the nearly circular, centrally symmetric case for all p strictly less than three, and that the inequality fails for all p strictly bigger than three.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics

Project
<a href="/en/project/GA21-07129S" target="_blank" >GA21-07129S: New Effects from Time-Reversal Non-Invariance</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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