Proof of time evolution integration theorems in calculus for moving surfaces
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David V. Svintradze
Abstract
We present a rigorous proof of the time evolution integration theorems that suitably extend differential geometry to the calculus of moving surfaces. This proof demonstrates that the calculus of moving surfaces is a complete extension of differential geometry to the dynamic manifolds.
Funding statement: This work was supported by the Shota Rustaveli Science Foundation of Georgia Grant No. STEM-22-365 (https://rustaveli.org.ge/eng), the European Commission’s ERC Erasmus+ collaborative linkage grant between the University of Copenhagen and New Vision University, the New Vision University’s internal funding and the Scholar in Residence Fulbright Scholarship for Professors 2024–2025.
Acknowledgements
We extend our gratitude to Thomas Rainer Heimburg for his insightful discussions and the generous hospitality provided by the Biocomplexity Department at the Niels Bohr Institute, University of Copenhagen. We also appreciate Martin Bier for coordinating the colloquium at East Carolina University’s Physics Department. We are grateful to Roland Duduchava, George Tephnadze, and Tengiz Buchukuri for encouraging us to contribute to mathematics, which is not our primary field. We would also like to dedicate this paper to Georgian mathematicians Nikoloz Muskhelishvili and Ilia Vekua, who remain largely unknown worldwide but are highly regarded in Georgia as the founders of a robust Georgian mathematical school. This paper is submitted to the Georgian Mathematical Journal to honor Georgia’s mathematical heritage.
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