Engineering Mechanics

Proceedings Vol. 31 (2025)

ENGINEERING MECHANICS 2025

31st INTERNATIONAL CONFERENCE
May 12 – 14, 2025, Medlov, Czech Republic

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Editors: Cyril Fischer and Jiří Náprstek

ISBN 978-80-86246-96-3 (printed)
ISBN 978-80-86246-99-4 (electronic)
ISSN 1805-8248 (printed)
ISSN 1805-8256 (electronic)

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Applications of Geometric Flows

Minarčík J.
pages 13 - 18, full text

Geometric flows describe the evolution of shapes driven by geometric quantities such as curvature. While originating in pure mathematics, where they played a central role in milestones like the proof of the Poincaré conjecture, these flows also have a rich history of applications across science and engineering. In this paper, we provide a brief overview of the key ideas behind geometric flows, focusing on curve and surface evolution in Euclidean space, and highlight their relevance to modeling dislocation lines in crystals, vortex filaments in fluids, and optimal structural forms in engineering. Our aim is to provide a concise but selfcontained exposition, emphasizing the conceptual beauty and broad utility of this mathematical framework.

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All papers were reviewed by members of the scientific committee.

Engineering Mechanics

International Conference

Proceedings Vol. 31 (2025)

ENGINEERING MECHANICS 2025