Index of minimal spheres and isoperimetric eigenvalue inequalities
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Publication:2225233
DOI10.1007/s00222-020-00992-5zbMath1503.53122arXiv1905.03174OpenAlexW3046213325MaRDI QIDQ2225233
Publication date: 5 February 2021
Published in: Inventiones Mathematicae (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1905.03174
Index theory and related fixed-point theorems on manifolds (58J20) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Twistor methods in differential geometry (53C28)
Related Items (18)
Spherical conical metrics and harmonic maps to spheres ⋮ Existence and classification of \(\mathbb{S}^1\)-invariant free boundary minimal annuli and Möbius bands in \(\mathbb{B}^n\) ⋮ On the Friedlander-Nadirashvili invariants of surfaces ⋮ Degenerating sequences of conformal classes and the conformal Steklov spectrum ⋮ The first eigenvalue of the Laplacian on orientable surfaces ⋮ Maximization of the second Laplacian eigenvalue on the sphere ⋮ Extremal metrics for combinations of Laplace eigenvalues and minimal surfaces into ellipsoids ⋮ On the index of the critical Möbius band in \(\mathbb{B}^4\) ⋮ A multiplicity estimate for the Jacobi operator of a nonflat Yang-Mills field over \(\mathbb{S}^m\) ⋮ On the index of minimal 2-tori in the 4-sphere ⋮ Existence of harmonic maps and eigenvalue optimization in higher dimensions ⋮ Continuity of eigenvalues and shape optimisation for Laplace and Steklov problems ⋮ An isoperimetric inequality for Laplace eigenvalues on the sphere ⋮ Large Steklov eigenvalues via homogenisation on manifolds ⋮ Existence of metrics maximizing the first eigenvalue on non-orientable surfaces ⋮ The second variation for null-torsion holomorphic curves in the 6-sphere ⋮ Robin spectrum: two disks maximize the third eigenvalue ⋮ Laplace and Steklov extremal metrics via \(n\)-harmonic maps
Cites Work
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- Sharp eigenvalue bounds and minimal surfaces in the ball
- The dimension and structure of the space of harmonic 2-spheres in the \(m\)-sphere
- Existence and regularity of maximal metrics for the first Laplace eigenvalue on surfaces
- Conformal upper bounds for the eigenvalues of the Laplacian and Steklov problem
- Upper bounds for eigenvalues of conformal metrics
- Index and flat ends of minimal surfaces
- Harmonic maps from surfaces to complex projective spaces
- Jacobi fields along harmonic 2-spheres in 3- and 4-spheres are not all integrable
- A unique extremal metric for the least eigenvalue of the Laplacian on the Klein bottle
- First-order twistor lifts
- The index of minimal immersions of \(S^ 2\) into \(S^{2n}\)
- Harmonic maps of the two-sphere into a complex Grassmann manifold. II
- On conformal minimal immersions of \(S^ 2\) into \({\mathbb{C}}P^ n\)
- Berger's isoperimetric problem and minimal immersions of surfaces
- A new conformal invariant and its applications to the Willmore conjecture and the first eigenvalue of compact surfaces
- Morse index and Gauss maps of complete minimal surfaces in Euclidean 3- space
- Extremal eigenvalues of the Laplacian in a conformal class of metrics: the `conformal spectrum'
- Isoperimetric inequality for the third eigenvalue of the Laplace-Beltrami operator on \(\mathbb{S}^2\)
- Metrics on a closed surface of genus two which maximize the first eigenvalue of the Laplacian
- Isoperimetric inequality for the second eigenvalue of a sphere.
- An isoperimetric inequality for the second non-zero eigenvalue of the Laplacian on the projective plane
- On branched minimal immersions of surfaces by first eigenfunctions
- On the Yang-Yau inequality for the first Laplace eigenvalue
- Spaces of harmonic maps of the projective plane to the four-dimensional sphere
- Variational aspects of Laplace eigenvalues on Riemannian surfaces
- Laplacian eigenvalue functionals and metric deformations on compact manifolds
- Minimal immersions of surfaces in Euclidean spheres
- Jacobi Fields Along Harmonic 2-Spheres in CP 2 are Integrable
- Harmonic maps of S 2 into a complex Grassmann manifold
- Equivariant Minimal Immersions of S 2 into S 2m (1)
- On Minimal Immersions of S 2 Into S 2m
- A Report on Harmonic Maps
- Second variation of superminimal surfaces into self-dual Einstein four-manifolds
- Harmonic 2-spheres with $r$ pairs of extra eigenfunctions
- Upper Bounds for the First Eigenvalue of the Laplacian on Non-Orientable Surfaces
- On the Existence of Metrics Which Maximize Laplace Eigenvalues on Surfaces
- Maximization of the second conformal eigenvalue of spheres
- Extremal Metric for the First Eigenvalue on a Klein Bottle
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