KFU. Card publication. Skew Minimal Surfaces Supported by Two Triangular Frames

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SKEW MINIMAL SURFACES SUPPORTED BY TWO TRIANGULAR FRAMES

Form of presentation

Articles in international journals and collections

Year of publication

2022

Язык

английский

Authors, employees of KFU

Alimov Mars Myasumovich, author

Bibliographic description in the original language

Alimov M.M., Skew Minimal Surfaces Supported by Two Triangular Frames//Russian Mathematics. - 2022. - Vol.66, Is.5. - P.1-20.

Annotation

An exact solution is constructed for the problem concerning the configuration of skew minimal surfaces supported by two equilateral triangular frames by applying the Chaplygin transform to hodograph variables. Skew appears due to a special arrangement of frames: they are not coaxial, but have central symmetry with respect to a certain point and mirror symmetry with respect to one of three planes formed by pairs of parallel bisectors belonging to the upper and lower frames. In the particular case of coaxial frames, our solution is compared with the known solution, which was found by the Weierstrass–Enneper representation.

Keywords

minimal surface, hodograph transformation, complex variable

The name of the journal

Russian Mathematics

Please use this ID to quote from or refer to the card

https://repository.kpfu.ru/eng/?p_id=278554&p_lang=2

Full metadata record

Field DC	Value	Language
dc.contributor.author	Alimov Mars Myasumovich	ru_RU
dc.date.accessioned	2022-01-01T00:00:00Z	ru_RU
dc.date.available	2022-01-01T00:00:00Z	ru_RU
dc.date.issued	2022	ru_RU
dc.identifier.citation	Alimov M.M., Skew Minimal Surfaces Supported by Two Triangular Frames//Russian Mathematics. - 2022. - Vol.66, Is.5. - P.1-20.	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/eng/?p_id=278554&p_lang=2	ru_RU
dc.description.abstract	Russian Mathematics	ru_RU
dc.description.abstract	An exact solution is constructed for the problem concerning the configuration of skew minimal surfaces supported by two equilateral triangular frames by applying the Chaplygin transform to hodograph variables. Skew appears due to a special arrangement of frames: they are not coaxial, but have central symmetry with respect to a certain point and mirror symmetry with respect to one of three planes formed by pairs of parallel bisectors belonging to the upper and lower frames. In the particular case of coaxial frames, our solution is compared with the known solution, which was found by the Weierstrass–Enneper representation.	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	minimal surface	ru_RU
dc.subject	hodograph transformation	ru_RU
dc.subject	complex variable	ru_RU
dc.title	Skew Minimal Surfaces Supported by Two Triangular Frames	ru_RU
dc.type	Articles in international journals and collections	ru_RU