We describe the potential functions for N= 4B supersymmetric quantum mechanics with D (2, 1; ) symmetry.

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We prove that the first Chern form of the moduli space of polarized Calabi-Yau manifolds, with the Hodge metric or the Weil-Petersson metric, represent the first Chern class of the canonical extensions of the tangent bundle to the compactification of the moduli space with normal crossing divisors.

We determine regularity results for energy minimizing maps from an n-dimensional Riemannian polyhedral complex X into a CAT(1) space. Provided that the metric on X is Lipschitz regular, we prove Hölder regularity with Hölder constant and exponent dependent on the total energy of the map and the metric on the domain. Moreover, at points away from the (n−2)-skeleton, we improve the regularity to locally Lipschitz. Finally, for points x ∈ X^{(k)} with k ≤ n−2, we demonstrate that the Hölder exponent depends on geometric and combinatorial data of the link of x ∈ X.

No abstract uploaded!