Since its introduction thanks to the work of Alexandrov, the method of moving planes has seen a widespread use in various applications of geometric analysis. Brought to the attention of the PDE community with the seminal work of Serrin, it has been a useful tool to prove a large variety of results, including symmetry results for overdetermined and rigidity problems. This thesis investigates three such problems from a quantitative viewpoint, by employing the method of moving planes and developing tools and techniques to prove symmetry and approximate symmetry results.
QUANTITATIVE STABILITY VIA THE METHOD OF MOVING PLANES: APPROXIMATE SYMMETRY FOR OVERDETERMINED AND RIGIDITY PROBLEMS / L. Pollastro ; tutor: G. Ciraolo, M. Cozzi ; coordinator: D. Bambusi. Dipartimento di Matematica Federigo Enriques, 2024 Mar 06. 36. ciclo, Anno Accademico 2022/2023.
QUANTITATIVE STABILITY VIA THE METHOD OF MOVING PLANES: APPROXIMATE SYMMETRY FOR OVERDETERMINED AND RIGIDITY PROBLEMS
L. Pollastro
2024
Abstract
Since its introduction thanks to the work of Alexandrov, the method of moving planes has seen a widespread use in various applications of geometric analysis. Brought to the attention of the PDE community with the seminal work of Serrin, it has been a useful tool to prove a large variety of results, including symmetry results for overdetermined and rigidity problems. This thesis investigates three such problems from a quantitative viewpoint, by employing the method of moving planes and developing tools and techniques to prove symmetry and approximate symmetry results.
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