Related papers: Smooth Blowups: Global vs. Local Perspectives

Real blow-ups and more refined "zooms" play a key role in the analysis of singularities of complex-analytic differential modules. They do not change the underlying topology, but the uniform structure. This suggests to revisit the cohomology…

Let $X$ be an oriented 4-manifold which does not have simple SW-type, for example a blow-up of a rational or ruled surface. We show that any two cohomologous and deformation equivalent symplectic forms on $X$ are isotopic. This implies that…

We exhibit a finite set of local moves that connect any two surgery presentations of the same 3-manifold via framed links in the three-sphere. The moves are handle-slides and blow-downs/ups of a particular simple kind.

This is a final step in a local classification of pseudo-Riemannian manifolds with parallel Weyl tensor that are not conformally flat or locally symmetric.

We give the parallelism between locally conformal symplectic manifolds and contact manifolds. We also give the generalization of exact contact manifolds.

We investigate several situations where the local homogeneity of a geometric structure on a dense open subset of a manifold implies the local homogeneity everywhere. This results in a strengthening of the conclusions in Gromov's open-dense…

We prove that the generalized rational blowdown, a surgery on smooth 4-manifolds, can be performed in the symplectic category.

Every open and orientable three manifold has a CR structure which is locally equivalent to the standard CR structure on $S^3$.

Blowup analysis for solutions of a general evolution equation with nonlocal diffusion and localized source is performed. By comparison with recent results on global-in-time solutions, a dichotomy result is obtained.

Using mixed analytical and numerical methods we investigate the development of singularities in the heat flow for corotational harmonic maps from the $d$-dimensional sphere to itself for $3\leq d\leq 6$. By gluing together shrinking and…

We propose nonlinear parabolic equations of Monge--Amp\'ere (M--A) type that admit regional, single poin, and global blow-up of similarity type. A similar model is derived for a fourth-order M--A flow.

Monotone polytopes, also known as smooth reflexive polytopes, are the polytopes associated to monotone symplectic toric manifolds and Gorenstein Fano toric varieties. We first show that the only monotone polytopes admitting blow-ups at…

The fourth-order quasilinear reaction-diffusion equation with a p-Laplacian operator is shown to admit three types of blow-up. Self-similar patterns are first constructed for the regional blow-up case, where the rescaled problem admits a…

Let (M,g) be a compact n-dimensional Riemannian manifold with boundary. This article is concerned with the set of scalar-flat metrics on M which are in the conformal class of g and have the boundary as a constant mean curvature…

Collision of equilibria with a splitting manifold has been locally studied, but might also be a contributing factor to global bifurcations. In particular a boundary collision can be coincident with collision of a virtual equilibrium with a…

We study the motion of a droplet evolving by mean curvature with volume constraint and contact angle condition on a half space. We prove the existence of a global-in-time weak solution, called the flat flow. A difficulty arises when we…

We consider the semilinear wave equation with subconformal power nonlinearity in two space dimensions. We construct a finite-time blow-up solution with an isolated characteristic blow-up point at the origin, and a blow-up surface which is…

A generalized-homology bordism-theory is constructed, such that for certain manifold homotopy stratified sets (MHSS; Quinn-spaces) homeomorphism-invariant geometric fundamental-classes exist. The construction combines three ideas: Firstly,…

In this paper we introduce a surgical procedure, called a rational blowdown, for a smooth 4-manifold X and determine how this procedure affects both the Donaldson and Seiberg-Witten invariants of X.

We consider the general problem of constructing the structure of a smooth manifold on a given space of loops in a smooth finite dimensional manifold. By generalising the standard construction for smooth loops, we derive a list of conditions…