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We provide new examples of K-unstable polarized smooth del Pezzo surfaces using a flopped version first used by Cheltsov and Rubinstein of the test configurations introduced by Ross and Thomas. As an application, we provide...
We provide new examples of K-unstable polarized smooth del Pezzo surfaces using a flopped version first used by Cheltsov and Rubinstein of the test configurations introduced by Ross and Thomas. As an application, we provide...
These surfaces may be seen as a...
These surfaces may be seen as a...
We consider a family of evolution equations that generalize the Peierls-Nabarro model for crystal dislocations. They can be seen as semilinear parabolic reaction-diffusion equations in which the diffusion is regulated by a...
In this paper we prove that, over a Hilbertian ground field, surfaces with two conic fibrations whose fibres have non-zero intersection product have the Hilbert property. We then give an application of this result, namely the...
We consider a family of evolution equations that generalize the Peierls-Nabarro model for crystal dislocations. They can be seen as semilinear parabolic reaction-diffusion equations in which the diffusion is regulated by a...
We construct finite time blow-up solutions to the 3-dimensional harmonic map flow into the sphere S2, ut = ∆u + |∇u|2u in Ω × (0, T) u = ub on ∂Ω × (0, T) u(·, 0) = u0 in Ω, with u(x, t)...
We construct finite time blow-up solutions to the 3-dimensional harmonic map flow into the sphere S2, ut = ∆u + |∇u|2u in Ω × (0, T) u = ub on ∂Ω × (0, T) u(·, 0) = u0 in Ω, with u(x, t)...
In this paper we prove that, over a Hilbertian ground field, surfaces with two conic fibrations whose fibres have non-zero intersection product have the Hilbert property. We then give an application of this result, namely the...
The nonlocal s-fractional minimal surface equation for Σ = ∂E where E is an open set in R N is given by H Σ s (p):= RN χE(x) − χEc(x ) dx = 0 for all p ∈ Σ. |x...
We consider the magnetic Ginzburg–Landau equations in R4 {−ε2(∇−iA)2u=[Formula presented](1−|u|2)u,ε2d⁎dA=〈(∇−iA)u,iu〉, formally corresponding to the...
The nonlocal s-fractional minimal surface equation for Σ = ∂E where E is an open set in R N is given by H Σ s (p):= RN χE(x) − χEc(x ) dx = 0 for all p ∈ Σ. |x...
We consider the energy-critical heat equation in ℝn for n ≥ 6 (Formula presented) which corresponds to the L2-gradient flow of the Sobolev-critical energy (Formula presented) Given any k ≥ 2 we find an...
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