Derives Clarke subdifferential and first-variation formula for the kth eigenvalue on self-adjoint operators (valid at essential spectrum edge) and applies it to characterize optimal weights in weighted Laplace/Steklov problems.
A new conformal invariant and its applications to the
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Constructs embedded flat minimal tori in odd codimensions q≥3 with constant S+λ₂ values dense in (2,3), providing counterexamples to Lu's second-gap conjecture.
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Eigenvalue optimization via a first-variation formula
Derives Clarke subdifferential and first-variation formula for the kth eigenvalue on self-adjoint operators (valid at essential spectrum edge) and applies it to characterize optimal weights in weighted Laplace/Steklov problems.