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Creators/Authors contains: "Cox, Graham"

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  1. ; ; ; (, Journal of the London Mathematical Society)
    Abstract A spectral minimal partition of a manifold is its decomposition into disjoint open sets that minimizes a spectral energy functional. It is known that bipartite spectral minimal partitions coincide with nodal partitions of Courant‐sharp Laplacian eigenfunctions. However, almost all minimal partitions are non‐bipartite. To study those, we define a modified Laplacian operator and prove that the nodal partitions of its Courant‐sharp eigenfunctions are minimal within a certain topological class of partitions. This yields new results in the non‐bipartite case and recovers the above known result in the bipartite case. Our approach is based on tools from algebraic topology, which we illustrate by a number of examples where the topological types of partitions are characterized by relative homology. 
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    Free, publicly-accessible full text available January 1, 2026
  2. ; ; ; (, SIAM Journal on Mathematical Analysis)
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  3. ; ; (, Mathematische Annalen)
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  4. ; ; ; (, Pure and Applied Analysis)
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  5. ; ; ; ; (, Annales de l'Institut Henri Poincaré C, Analyse non linéaire)
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  6. ; ; ; ; (, Mathematics of Wave Phenomena)
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  7. ; ; ; ; (, Annales mathématiques du Québec)
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  8. ; ; (, Letters in Mathematical Physics)
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  9. ; (, Journal of Differential Equations)
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