LONG-TERM BEHAVIOR OF CURVE SHORTENING FLOW IN R-3

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F20%3A00347570" target="_blank" >RIV/68407700:21340/20:00347570 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1137/19M1248522" target="_blank" >https://doi.org/10.1137/19M1248522</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/19M1248522" target="_blank" >10.1137/19M1248522</a>

Result language
angličtina
Original language name
LONG-TERM BEHAVIOR OF CURVE SHORTENING FLOW IN R-3
Original language description
Space curve motion describes dynamics of material defects or interfaces and can be found in image processing or vortex dynamics. This article analyzes some properties of space curves evolved by the curve shortening flow. In contrast to the classical case of shrinking planar curves, space curves do not obey the Avoidance principle in general. They can lose their convexity or develop noncircular singularities even if they are simple. In the first part of the text, we show that even though the convexity of space curves is not preserved during the motion, their orthogonal projections remain convex. In the second part, the Avoidance principle for spherical curves under the curve shortening flow in R-3 is shown by generalizing the arguments developed by Hamilton and Gage.
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/EF16_019%2F0000753" target="_blank" >EF16_019/0000753: Research centre for low-carbon energy technologies</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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