Related papers: A Matsusaka-type Theorem for Surfaces
Stokes theorem holds for Lipschitz forms on a smooth manifold.
In this article, we introduce the notion of good map and use it to establish Gromov-Witten theory for orbifolds.
The main objective of the paper is to prove a geometric version of sharp trace and product estimates on null hypersurfaces with finite curvature flux. These estimates play a crucial role to control the geometry of such null hypersurfaces.…
We give a formula in terms of multidimensional resultants for an equation for the flex locus of a projective hypersurface, generalizing a classical result of Salmon for surfaces. Using this formula, we compute the dimension of this flex…
The purpose of this note is to rephrase Speyer's elegant topological proof for Kasteleyn's Theorem in a simple graph theoretical manner.
In this paper we present some properties for projective hypersurfaces, smooth and singular, to be criteria for identification. To make the decision with these criteria, we have included procedures written in Singular language.
A generalization of the second main theorem of tropical Nevanlinna theory is presented for noncontinuous piecewise linear functions and for tropical hypersurfaces without requiring a growth condition. The method of proof is novel and…
We prove the existence of nontrivial closed surfaces with constant anisotropic mean curvature with respect to elliptic integrands in closed smooth $3$-dimensional Riemannian manifolds. The constructed min-max surfaces are smooth with at…
In this paper we give a new and simplified proof of the variational Hodge conjecture for complete intersection cycles on a hypersurface in projective space.
Understanding of the complex behavior of particles at surfaces requires detailed knowledge of both macroscopic and microscopic processes that take place; also certain processes depend critically on temperature and gas pressure. To link…
In this paper, we prove that for any smooth hypersurface $Y$ of degree $d$ in $\mathbb{P}^{n+1}_k$, the cyclic $d$-fold cover $\widetilde{Y} \to \mathbb{P}^{n+1}_k$ branched along $Y$ completely characterizes $Y$ up to projective…
We derive a generalized Stokes' theorem, valid in any dimension and for arbitrary loops, even if self intersecting or knotted. The generalized theorem does not involve an auxiliary surface, but inherits a higher rank gauge symmetry from the…
A novel generalization of photon surfaces to the case of massive charged particles is given for spacetimes with at least one isometry, including stationary ones. A related notion of glued massive particle surfaces is also defined. These…
We shall study stability conditions and Fourier-Mukai transforms on an elliptic surface. In particular we shall explain duality of elliptic surfaces by Fourier-Mukai transforms.
We determine the homeomorphism type of the set of real points of a smooth projective toric surface. This note may serve as an expository introduction to some of the ideas and techniques in C. Delaunay's work on real toric varieties.
This is an expository paper about applications of ruled surface theory in incidence geometry. It surveys the results that have been proven, gives an overview of the methods, and discusses some open problems and further directions. It will…
We give a generalization of Fujisawa's theorem in [F]. Our proof of the generalized theorem is purely algebraic and it is simpler than his proof.
In this paper, Clairaut's theorem is expressed on the surfaces of rotation in semi Euclidean 4-space. Moreover, the general equations of time-like geodesic curves are characterized according to the results of Clairaut's theorem on the…
The main goal of this paper is to give a general method to compute (via computer algebra systems) an explicit set of generators of the ideals of the projective embeddings of some ruled surfaces, namely projective line bundles over curves…
In this paper, we use the viewpoint of Gromov-Haustorff convergence to give some new comprehension of well known theorem,it is Huber's classification theorem\cite{Huber}\cite{MS}for complete Riemannian surfaces immersed in $\mathbb{R}^n$…