Conclusions about embedding singularities
They arise from a geometric constraint:
preferred metric
gaussian
curvature implies strong stretching penalty
thin Þ
singular
induced boundary edges, core
crescent
Novel features: singularities
interact strongly
energy condenses into
arbitrarily small fraction of system
singularities induce further
structure at large distanced
chaotic crumpled structure
hierarchical boundary waves
Fundamental puzzles
vanishing mean curvature at
forcing boundaries
generalization to other
metric-defined systems