Construction of Maxfaces with Infinitely Many Swallowtails and Planar Ends

Explore the construction of maxfaces featuring infinitely many swallowtails and planar ends in this 32-minute conference talk delivered at the International Centre for Theoretical Sciences. Learn advanced techniques for constructing these specialized minimal surfaces that exhibit both swallowtail singularities and planar end behaviors. Discover the mathematical framework underlying these complex geometric structures and understand how they contribute to the broader theory of minimal surfaces. Examine the analytical methods used to ensure the existence and properties of such surfaces with their distinctive infinite swallowtail configurations. Gain insights into the geometric analysis required to handle the intricate boundary conditions and singularity patterns that characterize these mathematical objects. This presentation forms part of the "Geometry and Analysis of Minimal Surfaces" program, connecting recent developments in minimal surface theory with applications across geometry, topology, complex analysis, and mathematical physics.