Date of Award
12-24-2025
Date Published
January 2026
Degree Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Mathematics
Advisor(s)
Jani Onninen
Abstract
In this dissertation, we are interested in a study of the minimizers to the $L^p$-mean distortion among Sobolev homeomorphisms $f:\mathbb T_*\to \mathbb T$ of finite distortion between embedded tori $\mathbb T = \mathbb T(R,r), \mathbb T_* = \mathbb T(R_*,r_*)$. For such mappings, the $L^p$-mean distortion for $1\le p < \infty$ is defined as \[ \int_{\mathbb T_*} K_f^p. \] We will show that the minimizer within a specific homotopy class to the $L^p$-mean distortion between embedded tori always exists. We will use free Lagrangians, whose integral only depends on the homotopy type of the function.
Access
Open Access
Recommended Citation
Krause, Adam, "Minimal Lp-Mean Distortion Maps between Embedded Tori" (2025). Dissertations - ALL. 2237.
https://surface.syr.edu/etd/2237
