arXiv research

The Wu-Yau theorem is proven for Sasakian manifolds with specific curvature conditions.

Recently Carr and Wu (2004, 2005) and also Huang and Wu (2004) show that most stochastic processes used in traditional option pricing models can be cast as special cases of time-changed Lévy processes. In particular these are models which can be tailored to exhibit correlated jumps in both the log price of assets and t…

Directly proves Wu's theorem on negative curvature metrics.

Examining when Wu-Yau inequalities reach their maximum values.

The Wu-Yau theorem is verified for negative curvature, and new examples of Kähler-Einstein metrics are found.

Motivated by the results of Wu-Yau-Zheng \cite{WuYauZheng}, we show that under a certain curvature assumption the harmonic representative of any boundary class of the Kähler cone is nonnegative.

In this paper, we study the uniqueness in the de Rham-Wu decomposition for pseudo-Riemannian manifolds.

An approach by J.Wu describes homotopy groups $π_{n}(S^2)$ of the standard 2-sphere as isotopy classes of spherical $n+1$--strand Brunnian braids is investigated in the case $n=3$ for applications.

The paper generalizes conditions for Euler characteristic and orientability of manifolds.

We develop a new approach to the classical problem on isotopy classification of embeddings of manifolds into Euclidean spaces. This approach involves studying of a new embedding invariant, of almost-embeddings and of smoothing, as well as explicit constructions of embeddings. Using this approach we obtain complete conc…

Paper defines new invariants from Khovanov homology, linking them to existing ones.

This paper is on homotopy classification of maps of (n+1)-dimensional manifolds into the n-dimensional sphere. For a continuous map f of an (n+1)-manifold into the n-sphere define the degree deg f to be the class dual to f^*[S^n], where [S^n] is the fundamental class. We present a short and direct proof of the followin…

We give an explicit calculation of the Wu invariants for immersions of a finite graph into the plane and classify all generic immersions of a graph into the plane up to regular homotopy by the Wu invariant. This result is a generalization of the fact that two plane curves are regularly homotopic if and only if they hav…

Classifies two families of simply connected 7-manifolds with minimal homological complexity.

Paper gives a full-twist inequality for a knot concordance invariant ν^+.

We study a class of Hermitian metrics on complex manifolds, recently introduced by J. Fu, Z. Wang and D. Wu, which are a generalization of Gauduchon metrics. This class includes the one of Hermitian metrics for which the associated fundamental 2-form is $\partial \bar\partial$-closed. Examples are given on nilmanifolds…

Decomposes Riemannian and Lorentzian manifolds for computing holonomy groups.

We introduce invariants of spatial graphs related to the Wu invariant and the Simon invariant, and apply them to prove that certain graphs are intrinsically chiral, and to obtain lower bounds for the minimal crossing number of embedded graphs.

New linear algorithms improve wSVMs for multiclass probability estimation.

Classifies invariant hypersurfaces with singularities.

Rediscovered by a systematic search, a forgotten class of integrable surfaces is shown to disprove the Finkel-Wu conjecture. The associated integrable nonlinear partial differential equation $z_{yy} + (1/z)_{xx} + 2 = 0$ possesses a zero curvature representation, a third-order symmetry, and a nonlocal transformatio…

New invariants from Heegaard Floer homology for knot concordance.

We show that a compact Kahler manifold with nonpositive holomorphic sectional curvature has nef canonical bundle. If the holomorphic sectional curvature is negative then it follows that the canonical bundle is ample, confirming a conjecture of Yau. The key ingredient is the recent solution of this conjecture in the pro…

Improved rigidity of Delaunay triangulated plane.

Introduces real bisectional curvature for Hermitian manifolds and classifies compact manifolds with constant curvature.

Paper addresses hybrid learning with constrained adversaries, achieving optimal performance.

Geodesic completeness proven for certain Lorentzian spaces.

WU-UCT parallelizes MCTS with linear speedup and limited performance loss.

In this paper, we shall use the Kähler geometry formulation to study the global behavior of the Ricci flow on $R^2$. The geometric feature of our Ricci flow is that it has finite width. Our aim is to determine the limiting metric (which corresponds an eternal Ricci flow) obtained by L.F.Wu. We can use the classificatio…

New ancient solutions to mean curvature flow in high dimensions identified.

The paper tackles prescribing discrete Gaussian curvature on polyhedral surfaces.

Determines regular homotopy classes for link immersions of simple singularities.

We generalize results of Lee, Gornik and Wu on the structure of deformed colored sl(N) link homologies to the case of non-generic deformations. To this end, we use foam technology to give a completely combinatorial construction of Wu's deformed colored sl(N) link homologies. By studying the underlying deformed higher r…

We define for each g>=2 and k>=0 a set M_{g,k} of orientable hyperbolic 3-manifolds with $k$ toric cusps and a connected totally geodesic boundary of genus g. Manifolds in M_{g,k} have Matveev complexity g+k and Heegaard genus g+1, and their homology, volume, and Turaev-Viro invariants depend only on g and k. In additi…

Study on eigenfunctions on sphere configurations, proving non-existence and construction of critical eigensections.

The paper extends Montel's theorem to complex Finsler manifolds.

Survey on recent breakthrough linking curvature and Kobayashi hyperbolicity.

Enhanced loop space decomposition for specific Poincaré complexes.

Cao's splitting theorem says that for any complete Kähler-Ricci flow $(M,g(t))$ with $t\in [0,T)$, $M$ simply connected and nonnegative bounded holomorphic bisectional curvature, $(M,g(t))$ is holomorphically isometric to $\C^k\times (N,h(t))$ where $(N,h(t))$ is a Kahler-Ricci flow with positive Ricci curvature for $t…

Compactness fails for curvature equations in high dimensions.

New method for sequential probability assignment reduces regret using contextual Shtarkov sums.

In [Wu], the noncommutative Atiyah-Patodi-Singer index theorem was proved. In this paper, we extend this theorem to the equivariant case.

Proves a similar inequality to a conjecture about hyperbolic space hypersurfaces.

We express the Connes-Chern character of the Dirac operator associated to a b-metric on a manifold with boundary in terms of a retracted cocycle in relative cyclic cohomology, whose expression depends on a scaling/cut-off pa- rameter. Blowing-up the metric one recovers the pair of characteristic currents that represent…

The comparison theory for the Riccati equation satisfied by the shape operator of parallel hypersurfaces is generalized to semi-Riemannian manifolds of arbitrary index, using one-sided bounds on the Riemann tensor which in the Riemannian case correspond to one-sided bounds on the sectional curvatures. Starting from 2-d…

Study automorphisms of pure braid groups on sphere homotopy groups.

The paper defines invariants for almost graph embeddings and explores their properties.

We show existence of unique smooth solutions to the Monge-Ampere equation for (n-1)-plurisubharmonic functions on Hermitian manifolds, generalizing previous work of the authors. As a consequence we obtain Calabi-Yau theorems for Gauduchon and strongly Gauduchon metrics on a class of non-Kahler manifolds: those satisfyi…