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Expositio paper exp-20260819-321582

On Minimal Surfaces

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This paper introduces Minimal Surfaces through the Weingarten Map and the 1st and 2nd Fundamental forms. Then, we consider two examples of a minimal surface, the catenoid and helicoid, verifying that both are indeed minimal surfaces through calculation. Final…

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exp-20260819-321582v1 Latest public version Public since August 20, 2026 Submitted August 19, 2026 0 saves
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Aleksei Lopatin (Kaleidoscope Circles)

Abstract

This paper introduces Minimal Surfaces through the Weingarten Map and the 1st and 2nd Fundamental forms. Then, we consider two examples of a minimal surface, the catenoid and helicoid, verifying that both are indeed minimal surfaces through calculation. Finally, we end with two theorems on minimal surfaces of revolution and ruled minimal surfaces and how they relate to the previous minimal surfaces in the examples.

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Mathematics
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Differential geometry Classical differential geometry Minimal surfaces in differential geometry, surfaces with prescribed mean curvature

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exp-20260819-321582v1

On Minimal Surfaces

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Uploaded Aug 19, 2026 417257 bytes Selected Latest
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