2025/12/21 by Anatoly Golberg, Vladimir Gutlyanskiî, Golberg, Anatoly +5
Mathematics · #30B75 #30C65 #31B15 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems
paper · doi:10.48550/arxiv.2512.18731
openalex publication_date 2025/12/21 · openalex created_date 2025/12/24 · openalex updated_date 2026/07/28
We explore the phenomenon of cavitation in higher-dimensional elasticity, defining it as the mapping of a punctured ball onto a non-degenerate ring domain. Crucially, for the class of locally quasiconformal mappings (or more general mappings) defined on the punctured ball 0<|x|<1 in \mathbb Rn that we examine, cavitation is equivalent to a failure of continuous extension to the origin. While existing modulus estimates prove insufficient for reliably detecting cavitation in this setting, our study establishes refined modulus bounds. This is achieved by introducing a novel directional dilatation which, in conjunction with the known angular dilatation, overcomes the limitations of previous methods. We illustrate our theoretical findings with several examples that demonstrate both cavitation occurrence and its absence.