Algebraic conditions identify special Lagrangian distributions in non-Kähler Calabi-Yau manifolds; explicit examples on Iwasawa and Nakamura manifolds yield non-diffeomorphic semi-flat SYZ mirror pairs.
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8 Pith papers cite this work. Polarity classification is still indexing.
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For M diffeomorphic to CP^n with scal_g ≥ 4n(n+1), sys_2^st(M,g) ≤ π with equality only for the Fubini-Study metric.
Constructs imaginary special Lagrangian cylinders near Maslov 0 or n intersections to obtain geodesics of positive Lagrangians and proves C^{1,1} regularity persistence under endpoint perturbations.
Constructs infinite-time singularities for Lagrangian mean curvature flow in Gibbons-Hawking spaces where H converges uniformly to 0 but log max |A| ~ sqrt(t) as t to infinity.
H-structures on closed manifolds are homotopy equivalent to their isometric classes via surjective metric map with lifting property, reducing to mapping spaces on parallelizable manifolds like tori, with applications to torsion energy flows.
Computes the right spectrum of the canonical G2-equivariant operator h, yielding slice-independent quartic curves and circles via SU(3) block decomposition after fixing complex slices in O.
A new extension-based construction produces strictly asymptotically Z-stable rank 3 bundles on polycyclic projective surfaces, plus a Hoppe-style criterion for rank 2 bundles.
A gluing theorem for ACyl associative submanifolds produces closed rigid associatives in twisted connected sum G2-manifolds with topologies S^3, RP^3 and RP^3#RP^3.
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Octonionic structure operator and its right spectrum
Computes the right spectrum of the canonical G2-equivariant operator h, yielding slice-independent quartic curves and circles via SU(3) block decomposition after fixing complex slices in O.