相关论文: The Stable Equivalence and Cancellation Problems
The main aim of this paper is to study existence and stability properties of rotationally symmetric proper biharmonic maps between two $m$-dimensional models (in the sense of Greene and Wu). We obtain a complete classification of…
The affine cancellation problem, which asks whether complex affine varieties with isomorphic cylinders are themselves isomorphic, has a positive solution for two dimensional varieties whose coordinate rings are unique factorization domains,…
A noncommutative analogue of the Zariski cancellation problem asks whether $A[x]\cong B[x]$ implies $A\cong B$ when $A$ and $B$ are noncommutative algebras. We resolve this affirmatively in the case when $A$ is a noncommutative finitely…
A thermodynamically consistent two-phase Stefan problem with temperature-dependent surface tension and with or without kinetic undercooling is studied. It is shown that these problems generate local semiflows in well-defined state…
We consider surjective endomorphisms f of degree > 1 on the projective n-space with n = 3, and f^{-1}-stable hypersurfaces V. We show that V is a hyperplane (i.e., deg(V) = 1) but with four possible exceptions; it is conjectured that deg(V)…
The aim of this work is to study homogeneous stable solutions to the thin (or fractional) one-phase free boundary problem. The problem of classifying stable (or minimal) homogeneous solutions in dimensions $n\geq3$ is completely open. In…
We study the stationary and axisymmetric non-convective differentially rotating perfect-fluid solutions of Einstein's field equations admitting one conformal symmetry. We analyse the two inequivalent Lie algebras not exhaustively considered…
We study stable solutions to the fractional Allen-Cahn equation \linebreak $(-\Delta)^{s/2} u = u-u^3$, $|u|<1$ in $\mathbb{R}^n$. For every $s\in (0,1)$ and dimension $n\geq 2$, we establish sharp energy estimates, density estimates, and…
The implications from the existence of a proper Homothetic Vector Field (HVF) on the dynamics of vacuum anisotropic models in $F(R)$ gravitational theory are studied. The fact that \emph{every} Spatially Homogeneous vacuum model is…
On a polarised surface, solutions of the Vafa-Witten equations correspond to certain polystable Higgs pairs. When stability and semistability coincide, the moduli space admits a symmetric obstruction theory and a $\mathbb C^*$ action with…
We classify the subvarieties of infinite dimensional affine space that are stable under the infinite symmetric group. We determine the defining equations and point sets of these varieties as well as the containments between them.
In this paper, we study the cohomology of vector bundles on projective space defined as kernels or cokernels of general maps $V_1 \to V_2$, where the $V_i$ are direct sums of line bundles or certain exceptional bundles. We prove an…
We construct a moduli space of stable projective pairs with a nontrivial action of a connected reductive group. These stable reductive pairs are higher-dimensional analogs of stable n-pointed curves and generalize to the non-commutative…
Given two irreducible curves of the plane which have isomorphic complements, it is natural to ask whether there exists an automorphism of the plane that sends one curve on the other. This question has a positive answer for a large family of…
Let $(V,q)$ be a vector bundle on a smooth projective curve $X$ together with a quadratic form $q: \mathrm{Sym}^2(V) \ra \mathcal{O}_X$ (respectively symplectic form $q: \Lambda^2V \ra \mathcal{O}_X$). Fixing the degeneracy locus of the…
A symmetric pair of reductive groups $(G,H,\theta)$ is called stable, if every closed double coset of $H$ in $G$ is preserved by the anti-involution $g\mapsto \theta(g^{-1})$. In this paper, we develop a method to verify the stability of…
We give a general structure theorem for affine A 1-fibrations on smooth quasi-projective surfaces. As an application, we show that every smooth A 1-fibered affine surface non-isomorphic to the total space of a line bundle over a smooth…
Let F_2 denote the free group of rank 2. Our main technical result of independent interest is: for any element u of F_2, there is g in F_2 such that no cyclically reduced image of u under an automorphism of F_2 contains g as a subword. We…
In this paper, we consider one-to-one matchings between two disjoint groups of agents. Each agent has a preference over a subset of the agents in the other group, and these preferences may contain ties. Strong stability is one of the…
We study a class of nonlocal double phase problems with discontinuous coefficients. A local self-improving property and a higher H\"older continuity result for weak solutions to such problems are obtained under the assumptions that the…