Publications

Journal Articles / Translation of mathematical literature

Variational Analysis of Generalized Elastic Catenaries under Constrained Energy Functionals: One-Dimensional Curves in Two and Three Dimensions and Tubular Surfaces in Three Dimensions (German)

Published in still not pubicly available, 2026

This article is intended for my participation in the Jugend Forscht competition next year and is currently not publicly available. The project is still being developed and refined. It has already presented the differential equation systems corresponding to three different cases. In this work, a fundamental theorem from measure theory is employed to improve and modify the classical catenary model by incorporating gravitational potential energy and torsional energy, rather than considering only bending energy.

Recommended citation: Yimu Mao. (2026). ".Variational Analysis of Generalized Elastic Catenaries under Constrained Energy Functionals: One-Dimensional Curves in Two and Three Dimensions and Tubular Surfaces in Three Dimensions "
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Topological Classification of Cubic Surfaces in Three-Dimensional Real Projective Space based on Julia Implementations: 5 Case Studies (German)

Published in TU Dresden, 2025

This article demonstrates how Julia and computer algebra tools classify topological types of real cubic surfaces in projective space. Developed during an internship at TU Dresden, it includes singularity computation, smoothness checks, and connected component counting for five examples. The code supports teaching and research.

Recommended citation: Yimu Mao. (2025). ".Topologische Klassifikation kubischer Flächen im dreidimensionalen reellen projektiven Raum anhand von Julia-Implementierungen: 5 Fallbeispiele "
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Analysis of Algebraic Varieties Using Galois Theory (German)

Published in Lübeck Jugend Forscht, 2025

This project explores the combination of algebraic geometry and Galois theory to determine the number of connected components of polynomial solution sets. Although the research is still in the development stage, several related methods have been introduced.

Recommended citation: Yimu Mao. (2025). ".Analyse algebraischer Varietäten mit Hilfe von Galois-Theorie "
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Triangle on Algebraic Curves (English)

Published in Christian-Albrechts-Universität zu Kiel Jugend Forscht, 2024

Originally inspired by ITYM competition Problem 9 (2023) source, this work was later developed into a research project submitted to the Jugend forscht competition in Germany.

Recommended citation: Yimu Mao. (2023). "Dreieck auf dem algebraische Kurven."
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