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Singular Minimal Surfaces which are Minimal

Universal Journal of Mathematics and Applications, 2021
In the present paper, we discuss the singular minimal surfaces in Euclidean $3-$space $\mathbb{R}^{3}$ which are minimal. Such a surface is nothing but a plane, a trivial outcome.
Ayla Erdur Kara, Muhittin Evren Aydın, Mahmut Ergüt   +2 more
doaj   +5 more sources

Family of Enneper Minimal Surfaces [PDF]

Mathematics, 2018
We consider a family of higher degree Enneper minimal surface E m for positive integers m in the three-dimensional Euclidean space E 3 . We compute algebraic equation, degree and integral free representation of Enneper minimal surface for
Erhan Güler
doaj   +2 more sources

Minimal nets and minimal minimal surfaces [PDF]

Acta Crystallographica Section A: Foundations and Advances, 2013
The 3-periodic nets of genus 3 (`minimal nets') are reviewed and their symmetries re-examined. Although they are all crystallographic, seven of the 15 only have maximum-symmetry embeddings if some links are allowed to have zero length. The connection between the minimal nets and the genus-3 zero-mean-curvature surfaces (`minimal minimal' surfaces) is ...
Olaf Delgado-Friedrichs, Stephen Hyde, Michael O'Keeffe   +2 more
exaly   +3 more sources

Triply periodic minimal surfaces for thermo-mechanical protection [PDF]

Scientific Reports
Triply periodic minimal surface (TPMS) metamaterials show promise for thermal management systems but are challenging to integrate into existing packaging with strict mechanical requirements. Composite TPMS lattices may offer more control over thermal and
Samantha Cheung, Jiyun Kang, Yujui Lin, Kenneth E. Goodson, Mehdi Asheghi, X. Wendy Gu   +5 more
doaj   +2 more sources

Crystal-Inspired Cellular Metamaterials and Triply Periodic Minimal Surfaces [PDF]

Biomimetics
Triply periodic minimal surfaces (TPMSs) are found in many natural objects including butterfly wings, sea urchins, and biological membranes. They simultaneously have zero mean curvature at every point and a crystallographic group symmetry. A metamaterial
Maxim Arsentev, Eduard Topalov, Sergey Balabanov, Evgenii Sysoev, Igor Shulga, Marsel Akhmatnabiev, Maxim Sychov, Ekaterina Skorb, Michael Nosonovsky   +8 more
doaj   +2 more sources

Porous polylactic acid scaffolds for bone regeneration: A study of additively manufactured triply periodic minimal surfaces and their osteogenic potential [PDF]

Journal of Tissue Engineering, 2020
Cecilia Persson, Anna Diez-Escudero
exaly   +2 more sources

Classification of Complete Regular Minimal Surfaces in ℝⁿ with Total Curvature −6π

Mathematics, 2022
In this paper, we classify the complete regular orientable minimal surfaces in Rn with total curvature −6π and give a method to construct a series of complete non-holomorphic minimal surfaces with total curvature −6π.
Minghao Li, Li Ou, Shuangcai Zhang
doaj   +1 more source

Wetting and minimal surfaces [PDF]

Physical Review E, 2007
22 ...
Bachas, Constantin, Doussal, Pierre Le, Wiese, Kay Jörg   +2 more
openaire   +6 more sources

Minimal surfaces for architectural constructions [PDF]

Facta Universitatis. Series: Architecture and Civil Engineering, 2008
Minimal surfaces are the surfaces of the smallest area spanned by a given boundary. The equivalent is the definition that it is the surface of vanishing mean curvature. Minimal surface theory is rapidly developed at recent time.
Velimirović Ljubica S., Radivojević Grozdana, Stanković Mića S., Kostić Dragan   +3 more
doaj   +1 more source

Minimal surfaces and weak gravity

Journal of High Energy Physics, 2020
We show that the Weak Gravity Conjecture (WGC) implies a nontrivial upper bound on the volumes of the minimal-volume cycles in certain homology classes that admit no calibrated representatives.
Mehmet Demirtas, Cody Long, Liam McAllister, Mike Stillman   +3 more
doaj   +1 more source