Curve shortening flow in a 3-dimensional pseudohermitian manifold
In this paper, we introduce a curve shortening flow in a 3-dimensional pseudohermitian manifold with vanishing torsion. The flow preserves the Legendrian condition and decreases the length of curves. The stationary solution of our flow is a Legendrian geodesic. We classify the singularity and prove...
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| Veröffentlicht in: | Calculus of variations and partial differential equations 2021-12, Vol.60 (6), Article 212 |
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| container_title | Calculus of variations and partial differential equations |
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| creator | Pan, Shujing Sun, Jun |
| description | In this paper, we introduce a curve shortening flow in a 3-dimensional pseudohermitian manifold with vanishing torsion. The flow preserves the Legendrian condition and decreases the length of curves. The stationary solution of our flow is a Legendrian geodesic. We classify the singularity and prove some convergence results. Moreover, we study the flow in Heisenberg group especially with Type
I
singularity. |
| doi_str_mv | 10.1007/s00526-021-02062-x |
| format | Article |
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I
singularity.</description><identifier>ISSN: 0944-2669</identifier><identifier>EISSN: 1432-0835</identifier><identifier>DOI: 10.1007/s00526-021-02062-x</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Analysis ; Calculus of Variations and Optimal Control; Optimization ; Control ; Mathematical and Computational Physics ; Mathematics ; Mathematics and Statistics ; Singularities ; Systems Theory ; Theoretical ; Three dimensional flow</subject><ispartof>Calculus of variations and partial differential equations, 2021-12, Vol.60 (6), Article 212</ispartof><rights>The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021</rights><rights>The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c249t-15bc48141f12321b90fabc48d457d858028a6861428cd4a203ebfd73524657fe3</citedby><cites>FETCH-LOGICAL-c249t-15bc48141f12321b90fabc48d457d858028a6861428cd4a203ebfd73524657fe3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00526-021-02062-x$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00526-021-02062-x$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Pan, Shujing</creatorcontrib><creatorcontrib>Sun, Jun</creatorcontrib><title>Curve shortening flow in a 3-dimensional pseudohermitian manifold</title><title>Calculus of variations and partial differential equations</title><addtitle>Calc. Var</addtitle><description>In this paper, we introduce a curve shortening flow in a 3-dimensional pseudohermitian manifold with vanishing torsion. The flow preserves the Legendrian condition and decreases the length of curves. The stationary solution of our flow is a Legendrian geodesic. We classify the singularity and prove some convergence results. Moreover, we study the flow in Heisenberg group especially with Type
I
singularity.</description><subject>Analysis</subject><subject>Calculus of Variations and Optimal Control; Optimization</subject><subject>Control</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Singularities</subject><subject>Systems Theory</subject><subject>Theoretical</subject><subject>Three dimensional flow</subject><issn>0944-2669</issn><issn>1432-0835</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp9kE1LAzEQhoMoWKt_wNOC52gy-djssRS_oOBFzyHdTdqU3aQmu1r_vVtX8OZhGBie92V4ELqm5JYSUt5lQgRITICOQyTgwwmaUc4AE8XEKZqRinMMUlbn6CLnHSFUKOAztFgO6cMWeRtTb4MPm8K18bPwoTAFw43vbMg-BtMW-2yHJm5t6nzvTSg6E7yLbXOJzpxps7363XP09nD_unzCq5fH5-VihWvgVY-pWNdcUU4dBQZ0XRFnjpeGi7JRQhFQRipJOai64QYIs2vXlEwAl6J0ls3RzdS7T_F9sLnXuzik8bOsQUjBFTBajhRMVJ1izsk6vU--M-lLU6KPqvSkSo-q9I8qfRhDbArlEQ4bm_6q_0l9A0Ama2M</recordid><startdate>20211201</startdate><enddate>20211201</enddate><creator>Pan, Shujing</creator><creator>Sun, Jun</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>JQ2</scope></search><sort><creationdate>20211201</creationdate><title>Curve shortening flow in a 3-dimensional pseudohermitian manifold</title><author>Pan, Shujing ; Sun, Jun</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c249t-15bc48141f12321b90fabc48d457d858028a6861428cd4a203ebfd73524657fe3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Analysis</topic><topic>Calculus of Variations and Optimal Control; Optimization</topic><topic>Control</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Singularities</topic><topic>Systems Theory</topic><topic>Theoretical</topic><topic>Three dimensional flow</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Pan, Shujing</creatorcontrib><creatorcontrib>Sun, Jun</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Computer Science Collection</collection><jtitle>Calculus of variations and partial differential equations</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Pan, Shujing</au><au>Sun, Jun</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Curve shortening flow in a 3-dimensional pseudohermitian manifold</atitle><jtitle>Calculus of variations and partial differential equations</jtitle><stitle>Calc. Var</stitle><date>2021-12-01</date><risdate>2021</risdate><volume>60</volume><issue>6</issue><artnum>212</artnum><issn>0944-2669</issn><eissn>1432-0835</eissn><abstract>In this paper, we introduce a curve shortening flow in a 3-dimensional pseudohermitian manifold with vanishing torsion. The flow preserves the Legendrian condition and decreases the length of curves. The stationary solution of our flow is a Legendrian geodesic. We classify the singularity and prove some convergence results. Moreover, we study the flow in Heisenberg group especially with Type
I
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| source | Springer Nature - Complete Springer Journals |
| subjects | Analysis Calculus of Variations and Optimal Control Optimization Control Mathematical and Computational Physics Mathematics Mathematics and Statistics Singularities Systems Theory Theoretical Three dimensional flow |
| title | Curve shortening flow in a 3-dimensional pseudohermitian manifold |
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