Related papers: A generalization of a completeness lemma in minima…
The notions of discrete conformality on triangle meshes have rich mathematical theories and wide applications. The related notions of discrete uniformizations on triangle meshes, suggest efficient methods for computing the uniformizations…
We discuss applications of minimal surfaces to comparison geometry.
We give a series of very general sufficient conditions in order to ensure the uniqueness of large solutions for --$\Delta$u + f (x, u) = 0 in a bounded domain $\Omega$ where f : $\Omega$ x R $\rightarrow$ R + is a continuous function, such…
We extend results on asymptotic invariants of line bundles on complex projective varieties to projective varieties over arbitrary fields. To do so over imperfect fields, we prove a scheme-theoretic version of the gamma construction of…
We provide a new foundational approach to the generalization of terms up to equational theories. We interpret generalization problems in a universal-algebraic setting making a key use of projective and exact algebras in the variety…
The goal of this paper is to study Yamabe flow on a complete Riemannian manifold of bounded geometry with possibly infinite volume. In the case of infinite volume, standard volume normalization of the Yamabe flow fails and the flow may not…
We prove a version of Linnik's basic lemma uniformly over the base field using theta-series and geometric invariant theory in the spirit of Khayutin's approach (Duke Math. J., 168(12), 2019). As an application, we establish entropy bounds…
The purpose of this note is to give an (esentially optimal) effective version of Matsusaka's Big theorem for smooth projective surfaces.
In this paper, we study the set of positive integers that characterize the universality of $m$-gonal form.
A direct proof of Oka's lemma on the relation of holomorphic convexity and the properties of the distance to the boundary function is provided. Some related problems for subharmonicity properties of this function are also studied. A new…
In this short note we establish an integral geometric inequality in a smooth metric measure space of the nonnegative Bakry-\'Emery Ricci curvature. This result can be regarded as a mild generalization of the almost Schur theorem due to De…
We prove compactness of solutions of a fully nonlinear Yamabe problem satisfying a lower Ricci curvature bound, when the manifold is not conformally diffeomorphic to the standard sphere. This allows us to prove the existence of solutions…
In this paper, we establish a weak version of the Kodaira vanishing theorem for surfaces in positive characteristic. As an application, we obtain some fundamental theorems in the minimal model theory for klt surfaces.
In this paper we consider an inverse problem of determining a minimal surface embedded in a Riemannian manifold. We show under a topological condition that if $\Sigma$ is a $2$-dimensional embedded minimal surface, then the knowledge of the…
We provide a simple proof of the radial symmetry of any nonnegative minimizer for a general class of quasi-linear minimization problems
This article explains and extends semialgebraic homotopy theory (developed by H. Delfs and M. Knebusch) to o-minimal homotopy theory (over a field). The homotopy category of definable CW-complexes is equivalent to the homotopy category of…
In 1987, Yomdin proved a lemma on smooth parametrizations of semialgebraic sets as part of his solution of Shub's entropy conjecture for $C^\infty$ maps. The statement was further refined by Gromov, producing what is now known as the…
In continuing the study of harmonic mapping from 2-dimensional Riemannian simplicial complexes in order to construct minimal surfaces with singularity, we obtain an a-priori regularity result concerning the real analyticity of the free…
Haga's fold in paper folding is generalized. Recent generalization of Haga's theorems and problems in Wasan geometry involving Haga's fold are also generalized.
In this paper, we consider a Generalized Bernstein Theorem for a type of generalized minimal surfaces, namely minimal Plateau surfaces. We show that if an orientable minimal Plateau surface is stable and has quadratic area growth in…