Analysis · Oct 6, 2026

Fourier restriction for positively curved surfaces

Proves the diagonal Fourier extension conjecture for positively curved surfaces in three dimensions. For every compact smooth positively curved surface Σ⊂R3\Sigma\subset\mathbb R^3, including surfaces with boundary, the extension operator is bounded from Lp(Σ)L^p(\Sigma) to Lp(R3)L^p(\mathbb R^3) for every p > 3.

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