Explore more content. Shape transformations in optically trapped particles and minimal surfaces: An experimental and theoretical study. Cite Download Optical tweezing can be used to isolate single, micrometre sized particles.
Graduate Thesis Defenses 2019
 Fractional Perimeter and Nonlocal Minimal Surfaces
PhD thesis, University of Warwick. Request Changes to record. Our work is concerned with the relation between a complex differential geometric property, namely holomorphicity, and a metric one, namely to be conformal and minimal, of immersions possibly branched of Riemann surfaces into Kahler manifolds. A well known theorem Wirtinger's Inequality states that every holomorphic surface inside a Kahler manifold is area minimizing w. Of course, the converse is not true in general. However, there are important situations, as in the resolution of the Frankel Conjecture by Siu and Yau, when it is. A first motivation for our research is to understand to which extent is the converse true.
Triply periodic minimal surface
This book starts with the classical theory of minimal surfaces and ends up with current research topics. Of the various ways of approaching minimal surfaces from complex analysis, PDE, or geometric measure theory , the authors have chosen to focus on the PDE aspects of the theory. The book also contains some of the applications of minimal surfaces to other fields including low dimensional topology, general relativity, and materials science. The only prerequisites needed for this book are a basic knowledge of Riemannian geometry and some familiarity with the maximum principle.
Here is a list of subject matters for possible thesis at the level of bachelor or master. Sard's Theorem following: Section 3. Level: easy The lemniscate and elliptic integrals following: starting with Wikipedia here , here , and here. Math involved: basic differential geometry. Level: easy Ruled surfaces and minimal surfaces following: Section 3.