Stability of Helical Edge Modes in Triangular Antiferromagnets along Curved Boundaries

We explore helical edge modes in triangular antiferromagnets that propagate along curved boundaries. We develop a technique based on conformal mappings, which allows us to transform various geometries into equivalent straight boundaries. Using this approach, we identify the conditions under which these edge modes are robust and exhibit long lifetimes in curved geometries. This technique also provides a broadly applicable framework for studying edge modes in other two-dimensional systems with complex boundary geometries, particularly in 2+1-dimensional settings where boundary effects are essential for understanding low-energy behaviors.