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Existence of metrics maximizing the first Laplace eigenvalue on closed surfaces
Mikhail Karpukhin, Romain Petrides, Daniel Stern
Building on seminal work of Nadirashvili and previous work of the authors, we prove the existence of metrics maximizing the area-normalized first eigenvalue of the Laplacian on eve…
Embedded minimal surfaces in and via equivariant eigenvalue optimization
Mikhail Karpukhin, Robert Kusner, Peter McGrath +1
In 1970, Lawson solved the topological realization problem for minimal surfaces in the sphere, showing that any closed orientable surface can be minimally embedded in $\mathbb{S}^3…
Dirac Eigenvalue Optimisation and Harmonic Maps to Complex Projective Spaces
Mikhail Karpukhin, Antoine Métras, Iosif Polterovich
Consider a Dirac operator on an oriented compact surface endowed with a Riemannian metric and spin structure. Provided the area and the conformal class are fixed, how small can the…
Existence of harmonic maps and eigenvalue optimization in higher dimensions
Mikhail Karpukhin, Daniel Stern
We prove the existence of nonconstant harmonic maps of optimal regularity from an arbitrary closed manifold of dimension to any closed, non-aspherical manifold …