相关论文: A holomorphic representation formula for parabolic…
We classify isoparametric hypersurfaces in complex hyperbolic spaces.
We construct examples of inhomogeneous isoparametric real hypersurfaces in complex hyperbolic spaces.
We construct a new representation formula for indefinite improper affine spheres in terms of two para-holomorphic functions and study singularities which appear in this representation formula. As a result, it follows that cuspidal cross…
Isoparametric hypersurfaces and their application to special geometries
We give a local representation for the pseudoholomorphic surfaces in Euclidean spheres in terms of holomorphic data. Similar to the case of the generalized Weierstrass representation of Hoffman and Osserman, we assign such a surface in…
The theory of stochastic representations of solutions to elliptic and parabolic PDE has been extensive. However, the theory for hyperbolic PDE is notably lacking. In this short note we give a stochastic representation for solutions of…
We derive an explicit formula for the volume of a regular simplex in the hyperbolic space of any dimension.
We discuss non-conformal harmonic surfaces in $R^3$ with prescribed ($\pm$)transforms, and we get a representation formula for non-conformal harmonic surfaces in $R^3$.
We show a mass formula for arbitrary supersingular abelian surfaces in characteristic $p$.
We present a representation formula for discrete indefinite affine spheres via loop group factorizations. This formula is derived from the Birkhoff decomposition of loop groups associated with discrete indefinite affine spheres. In…
This article simply presents several coordinate systems for 2 and 3-dimensional hyperbolic spaces, describing the general solutions of Helmholtz equation in each one of these systems.
H\"older estimates for second derivatives are proved for solutions of fully nonlinear parabolic equations in two space variables. Related techniques extend the regularity theory for fully nonlinear parabolic equations in higher dimensions.
We present an explicit expression of the anomaly formula for the Cappell-Miller holomorphic torsion for K\"{a}hler manifolds.
In this paper, we prove restriction estimates for hyperbolic paraboloids in dimensions $n>=5$ by the polynomial partitioning method.
We give a new representation formula for solutions to nonconvex first-order Hamilton--Jacobi equations in the periodic setting and present some applications. We then prove the large time behavior for solutions under some additional…
See math.CV/0509030 which replaces this paper.
This paper presents a unified theory for the power of a point with respect to generalized spheres (spheres, horospheres, and hyperspheres) in $n$-dimensional hyperbolic space $\mathbf{H}^n$. By extending the classical secant theorem, we…
In this paper, we present series representations of the remainders in the expansions for certain trigonometric and hyperbolic functions. By using the obtained results, we establish some inequalities for trigonometric and hyperbolic…
A complete invariant and a binary combination for irreducible representations of SL2(R) are introduced. With this, a new two-parameter family of representations is defined.
We discuss asymptotically hyperbolic manifold with a noncompact boundary which is close to a horosphere in a certain sense. The model case is a horoball or the complement of a horoball in standard hyperbolic space. We show some geometric…