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pro vyhledávání: '"Waldron, Alex"'
Autor:
Waldron, Alex
We prove a Lojasiewicz-Simon inequality $$ \left| E(u) - 4\pi n \right| \leq C \| \mathcal{T}(u) \|^\alpha $$ for maps $u \in W^{2,2}\left( S^2, S^2 \right).$ The inequality holds with $\alpha = 1$ in general and with $\alpha > 1$ unless $u$ is nearl
Externí odkaz:
http://arxiv.org/abs/2312.16686
Autor:
Waldron, Alex
A finite-time singularity of 2D harmonic map flow will be called "strictly type-II" if the outer energy scale satisfies $\lambda(t) = O(T - t)^{\frac{1 + \alpha}{2}}.$ We prove that the body map at a strict type-II blowup is H\"older continuous.
Externí odkaz:
http://arxiv.org/abs/2112.14255
Autor:
Song, Chong, Waldron, Alex
Let $\Sigma$ be a compact oriented surface and $N$ a compact K\"ahler manifold with nonnegative holomorphic bisectional curvature. For a solution of harmonic map flow starting from an almost-holomorphic map $\Sigma \to N$ (in the energy sense), the l
Externí odkaz:
http://arxiv.org/abs/2009.07242
Autor:
Waldron, Alex
Publikováno v:
Jour. London Math. Soc. 106(4), 3711-3745 (2022)
We study the deformation theory of $\mathrm{G}_2$-instantons on the 7-sphere, specifically those obtained from instantons on the 4-sphere via the quaternionic Hopf fibration. We find that the pullback of the standard ASD instanton lies in a smooth, c
Externí odkaz:
http://arxiv.org/abs/2002.02386
Autor:
Oliveira, Goncalo, Waldron, Alex
Publikováno v:
Adv. math. 376, 107418 (2021)
This paper develops Yang-Mills flow on Riemannian manifolds with special holonomy. By analogy with the second-named author's thesis, we find that a supremum bound on a certain curvature component is sufficient to rule out finite-time singularities. A
Externí odkaz:
http://arxiv.org/abs/1812.10866
Autor:
Waldron, Alex
This paper proves a general Uhlenbeck compactness theorem for sequences of solutions of Yang-Mills flow on Riemannian manifolds of dimension $n \geq 4,$ including rectifiability of the singular set at finite or infinite time.
Comment: Final vers
Comment: Final vers
Externí odkaz:
http://arxiv.org/abs/1812.10863
Autor:
Waldron, Alex
We investigate the long-time behavior and smooth convergence properties of the Yang-Mills flow in dimension four. Two chapters are devoted to equivariant solutions and their precise blowup asymptotics at infinite time. The last chapter contains gener
Autor:
Waldron, Alex
Publikováno v:
Invent. math. 217(3), 1069-1147 (2019)
We establish that finite-time singularities do not occur in four-dimensional Yang-Mills flow, confirming the conjecture of Schlatter, Struwe, and Tahvildar-Zadeh. The proof relies on a weighted energy identity and sharp decay estimates in the neck re
Externí odkaz:
http://arxiv.org/abs/1610.03424
Autor:
Oliveira, Gonçalo, Waldron, Alex
Publikováno v:
In Advances in Mathematics 6 January 2021 376
Autor:
Waldron, Alex
Publikováno v:
Calc. Var. 55(5), 1-31 (2016)
Several results on existence and convergence of the Yang-Mills flow in dimension four are given. We show that a singularity modeled on an instanton cannot form within finite time. Given low initial self-dual energy, we then study convergence of the f
Externí odkaz:
http://arxiv.org/abs/1402.3224