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Rotation Bounds for Hölder Continuous Homeomorphisms with Integrable Distortion.

A Clop1, L Hitruhin2, B Sengupta3

  • 1Department of Mathematics and Computer Science, Universitat de Barcelona, 08007 Barcelona, Catalonia Spain.

Journal of Geometric Analysis
|June 1, 2022
PubMed
Summary
This summary is machine-generated.

This study establishes precise rotation bounds for specific homeomorphisms with finite distortion, enhancing existing mathematical theories. These findings offer sharper insights into the behavior of these functions, with implications for fluid mechanics.

Keywords:
Mappings of finite distortionQuasiconformal mapsRotation bounds

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Area of Science:

  • Complex analysis
  • Geometric function theory
  • Partial differential equations

Background:

  • Homeomorphisms of finite distortion are crucial in geometric analysis.
  • Existing rotation bounds have limitations, particularly regarding the Hölder continuity of inverses.
  • Applications in fluid mechanics highlight the need for refined bounds.

Purpose of the Study:

  • To derive sharp rotation bounds for a specific subclass of homeomorphisms of finite distortion.
  • To investigate the role of Hölder continuous inverses in obtaining these bounds.
  • To improve upon existing rotation bounds in the literature.

Main Methods:

  • Analysis of homeomorphisms with distortion functions in L^p spaces.
  • Utilizing the property of Hölder continuous inverses.
  • Developing novel techniques to establish sharp rotation bounds.

Main Results:

  • Obtained sharp rotation bounds for homeomorphisms of finite distortion with Hölder continuous inverses.
  • Demonstrated that these bounds are an improvement over previous results.
  • Provided examples that confirm the sharpness of the derived bounds.

Conclusions:

  • The Hölder continuity of the inverse is key to achieving sharper rotation bounds.
  • The new bounds offer a significant advancement in the study of finite distortion homeomorphisms.
  • The results have potential applications in areas like fluid mechanics.