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In this paper, we investigate the geometry of base complex manifold an effectively parametrized holomorphic family stable Higgs bundles over a fixed compact K\"{a}hler manifold. The starting point our study is Schumacher-Toma/Biswas-Schumacher's curvature formulas for Weil-Petersson-type metrics, in Sect. 2, give some applications their on geometric properties 3, calculate higher direct image b...

This paper analyses the convergence and degeneration of sequences of metrics on a 3-manifold, and relations of such with Thurston’s geometrization conjecture. The sequences are minimizing sequences for a certain (optimal) scalar curvature-type functional and their degeneration is related to the sphere and torus decompositions of the 3-manifold under certain conditions.

Let X be a compact Kähler manifold and let L be a pseudoeffective line bundle on X with singular metric φ. We first define a notion of numerical dimension of the pseudo-effective pair (L,φ) and then discuss the properties of it. We prove also a very general KawamataViehweg-Nadel type vanishing theorem on an arbitrary compact Kähler manifold.

Using elementary counting methods, we calculate the universal invariant (also known as the LMO invariant) of a 3-manifold M , satisfying H1(M,Z) = Z, in terms of the Alexander polynomial of M . We show that +1 surgery on a knot in the 3-sphere induces an injective map from finite type invariants of integral homology 3-spheres to finite type invariants of knots. We also show that weight systems ...

In this paper, we study the Nyström type subsampling for large scale kernel methods to reduce the computational complexities of big data. We discuss the multi-penalty regularization scheme based on Nyström type subsampling which is motivated from well-studied manifold regularization schemes. We develop a theoretical analysis of multi-penalty least-square regularization scheme under the general ...

We prove a CR version of the Obata’s result for the first eigenvalue of the sub-Laplacian in the setting of a compact strictly pseudoconvex pseudohermitian three dimensional manifold with non-negative CR-Paneitz operator which satisfies a Lichnerowicz type condition. We show that if the first positive eigenvalue of the sub-Laplacian takes the smallest possible value then, up to a homothety of t...