Related papers: On Bloch's Theorem for Heat Maps
In this paper, we study the existence of fixed points for mappings defined on complete metric space (X, d) satisfying a general contractive inequality of integral type depended on another function. This conditions is analogous of Banach…
We establish global existence of smooth solutions to heat flow for Yang-Mills-Higgs functional on Kahler fibrations. As an application, we give a new proof of the key inequality for Mundet's Hitchin-Kobayashi correspondence theorem using…
We introduce and study a conformal heat flow of harmonic maps defined by an evolution equation for a pair consisting of a map and a conformal factor of metric on the two-dimensional domain. This flow is designed to postpone finite time…
We establish existence of global-in-time weak solutions to the one dimensional, compressible Navier-Stokes system for a viscous and heat conducting ideal polytropic gas (pressure $p=K\theta/\tau$, internal energy $e=c_v \theta$), when the…
Using Bloch-Ogus theorem and Chern character from K-theory to cyclic homology, we answer a question of Green and Griffiths on extending Bloch formula. Moreover, we construct a map from local Hilbert functor to local cohomology. With…
In the present paper, a new type of mappings called perimetric contractions on $k$-polygons is introduced. These contractions can be viewed as a generalization of mappings that contracts perimeters of triangles. A fixed point theorem for…
Assume that $A$ is a closed linear operator defined on all of a Hilbert space $H$. Then $A$ is bounded. A new short proof of this classical theorem is given on the basis of the uniform boundedness principle. The proof can be easily extended…
We study one-dimensional viscoelastic phase transitions modeled by a Ginzburg--Landau energy with a non-convex cubic stress-strain law. Extending the isothermal model, we couple the momentum equation to a heat equation for the temperature…
The aim of this note is to present the simple observation that a slight refinement of the Contraction Mapping Principle allows one to recover the precise convergence rate in the Picard-Lindel\"of Theorem.
In this short note we give some corollaries of the polynomial inverse function theorem for large fields. We prove inverse and implicit function theorems for Nash maps over large fields, characterize large fields as fields satisfying inverse…
The notion of $p$-summing Bloch mapping from the complex unit open disc $\mathbb{D}$ into a complex Banach space $X$ is introduced for any $1\leq p\leq\infty$. It is shown that the linear space of such mappings, equipped with a natural…
Let X be a complex surface with no nontrivial 2-forms. Then we show that Bloch's conjecture is true (i.e. the Albanese map in this case is injective) if and only if any homologically trivial idempotent in the ring of correspondences…
In this article we discuss a possibility to implement a well-known scheme of proof for contraction mapping theorems in a situation, when convergence, families of Cauchy sequences, and contractiveness of mappings are defined axiomatically.…
In this paper, we consider three typical problems on a locally finite connected graph. The first one is to study the Bochner formula for the Laplacian operator on a locally finite connected graph. We use the Bochner formula to derive the…
We study the Cauchy problem with periodic initial data for the forward-backward heat equation defined by the J-self-adjoint linear operator L depending on a small parameter. The problem has been originated from the lubrication approximation…
In this note we report local well-posedness results for the Cauchy problems associated to generalized KdV type equations with dissipative perturbation for given data in the low regularity $L^2$-based Sobolev spaces. The method of proof is…
We prove a fixed point theorem that combines the contraction mapping principle and some Knaster-Tarski-like theorem. As a consequence we obtain an existence theorem to initial value problem for ordinary differential equation with…
In this paper, we study the existence of fixed points for mappings defined on complete (compact) metric space (X, d) satisfying a general contractive (contraction) inequality depended on another function. These conditions are analogous to…
In this paper, we first establish Landau-Bloch-type theorems for poly $(K,K')$-elliptic harmonic mappings, which are sharp in some given cases. Thereafter, we provide several coefficient bounds for $(K,K')$-elliptic and $K$-quasiregular…
In this paper, we present an alternate, elementary proof of the local Lipschitz regularity of the suitable weak solution of heat flow of harmonic maps into CAT(0)-metric spaces, whose existence was established by Lin, Segatti, Sire, and…