Related papers: Smooth solutions to the complex Plateau problem
The first two authors [Proc. Lond. Math. Soc. (3) {\bf 114}(1):1--34, 2017] classified the behaviour near zero for all positive solutions of the perturbed elliptic equation with a critical Hardy--Sobolev growth $$-\Delta u=|x|^{-s}…
In this paper, we give some examples of area minimizing surfaces to clarify some well-known features of these surfaces in more general settings. The first example is about Meeks-Yau's result on embeddedness of solution to the Plateau…
We show that six-dimensional backgrounds that are T^2 bundle over a Calabi-Yau two-fold base are consistent smooth solutions of heterotic flux compactifications. We emphasize the importance of the anomaly cancellation condition which can…
We consider the question if a five dimensional manifold can be embedded into a Calabi-Yau manifold of complex dimension three such that the real part of the holomorphic volume form induces a given closed 3-form on the 5-manifold. We define…
We identify the twisted sectors of a compact simplicial toric variety. We do the same for a generic nondegenerate Calabi-Yau hypersurface of an $n$-dimensional simplicial Fano toric variety and then explicitly compute $h^{1,1}_{orb}$ and…
This is the first of a series of papers in which we systematically use singularity theory to study four dimensional N=2 superconformal field theories. Our main focus in this paper is to identify what kind of singularity is needed to define…
We study the Gepner model description of D-branes in Calabi-Yau manifolds with singular curves. From a geometrical point of view, the resolution of singularities leads to additional homology cycles around which branes can wrap. Using…
We prove that strictly hyperbolized smooth cube manifolds admit normal smooth structures.
We construct D=10 supergravity solutions corresponding to type IIB fivebranes wrapping a two-sphere in a Calabi-Yau two-fold. These are related in the IR to the large N limit of pure N=2 SU(N) super Yang-Mills theory. We show that the…
We apply Garnier's method to solve the Plateau problem for maximal surfaces in Minkowski 3-space. Our study relies on the improved version we gave of R. Garnier's resolution of the Plateau problem for polygonal boundary curves in Euclidean…
We prove a new rigidity criterion for families of polarized Calabi-Yau manifolds. Motivated by known non-rigid examples, we conjecture that a family over a quasi-projective curve is rigid if it admits a smooth compactification whose…
We simplify some technical steps from \cite{S1} in which a conjecture of De Giorgi was addressed. For completeness we make the paper self-contained and reprove the classification of certain global bounded solutions for semilinear equations…
The complex Plateau problem is analogous, in a Hermitian complex manifold, to the classical Plateau problem in 3 dimensional real space: it is a geometrical problem of extension of a closed real manifold into a complex analytic subvariety,…
We show that the Hilbert polynomial of a Calabi-Yau hypersurface $Z$ in a smooth toric variety $M$ associated to a convex polytope $\Delta$ is given by a lattice point count in the polytope boundary $\partial \Delta,$ just as the Hilbert…
Given a closed oriented manifold or more generally a group homology class, we introduce the spherical Plateau problem, which is a variational problem corresponding to a topological invariant called the spherical volume. In principle, its…
We consider the Cauchy problem with smooth data for compressible Euler equations in many dimensions and concentrate on two cases: solutions with finite mass and energy and solutions corresponding to a compact perturbation of a nontrivial…
We consider the group theoretical properties of R--R scalars of string theories in the low-energy supergravity limit and relate them to the solvable Lie subalgebra $\IG_s\subset U$ of the U--duality algebra that generates the scalar…
Greene, Morrison and Plesser \cite{GMP} have recently suggested a general method for constructing a mirror map between a $d$-dimensional Calabi-Yau hypersurface and its mirror partner for $d > 3$. We apply their method to smooth…
This paper is a continuation of hepth/0507224 where open topological B-models describing D-branes on 2-cycles of local Calabi--Yau geometries with conical singularities were studied. After a short review, the paper expands in particular on…
We construct new static, spherically symmetric non-extremal black hole solutions of four-dimensional ${\cal N}=2$ supergravity, using a systematic technique based on dimensional reduction over time (the c-map) and the real formulation of…