Higher Genus Maxfaces with Arbitrarily Many Catenoid or Planar Ends

Explore the construction and properties of higher genus maxfaces featuring arbitrarily many catenoid or planar ends in this 30-minute conference talk. Delve into advanced topics in minimal surface theory as part of the "Geometry and Analysis of Minimal Surfaces" program at the International Centre for Theoretical Sciences. Learn about the geometric and analytic aspects of these specialized minimal surfaces, which represent significant developments in understanding complex surface structures. Examine the mathematical techniques used to construct maxfaces with multiple ends, focusing on both catenoid and planar configurations. Discover how these surfaces contribute to the broader field of minimal surface theory, connecting concepts from geometry, topology, complex analysis, and partial differential equations. Gain insights into cutting-edge research that bridges theoretical mathematics with applications in architecture, biology, and material science.