Higher order Yang-Mills flow

Kelleher, Casey Lynn

doi:10.48550/arxiv.1505.07092

Cited by 2 publications

(9 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Furthermore, when n = 2(k + 2) we cannot rule out finite time singularities, but we show that if present, they are due to an L k+2 curvature concentration phenomenon, see proposition 8.3 and theorem 8.4. This is analogous to what Kelleher observes for the higher order Yang-Mills flow (theorem B [8]). However, this is in contrast with the work of Hong and Schabrun (theorem 1 in [5]) and Schabrun (theorem 1 in [15]), on the Seiberg-Witten flow, who are able to show that an L 2 curvature concentration phenomenon can obstruct long time existence, but are able to rule out such concentration by a careful rescaling argument together with an L 2 energy estimate.…”

Section: Introductionsupporting

confidence: 83%

“…The above theorem can be seen as an analogue of the first part of theorem 7.8 in [10], and theorem A in [8], for the case of these higher order Seiberg-Witten functionals. 8.2.…”

Section: Long Time Existence Resultsmentioning

confidence: 80%

“…Finally, we will need the following interpolation result, see corollary 5.5 in [8], and corollary 5.3 in [9]. Lemma 10.3.…”

Section: Long Time Existence Resultsmentioning

confidence: 99%

“…We start with the Weitzenböck identity, see theorem 9.4.1 in [13]. The following lemma tells us how to switch derivatives, see lemma 5.12 in [8]. The second theorem we will need is a theorem that allows us to glue together a sequence of connections defined on small open sets, see corollary 4.4.8 [2].…”

Section: Long Time Existence Resultsmentioning

confidence: 99%

“…He is able to show (theorem 7.8 [10]), that provided the derivatives in his functionals are large enough, singularities in finite time do not occur. Inspired by this, Kelleher in [8] considers a higher order variant of the Yang-Mills flow. She proves long time existence in sub-critical dimensions (theorem A in [8]), and is able to prove a curvature concentration phenomenon in the critical dimension (theorem B [8]), analogous to the result obtained by Struwe (theorem 2.3 [18]) for the Yang-Mills flow in dimension four.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Higher order Seiberg–Witten functionals and their associated gradient flows

Saratchandran

2018

manuscripta math.

View full text Add to dashboard Cite

We define functionals generalising the Seiberg-Witten functional on closed spin c manifolds, involving higher order derivatives of the curvature form and spinor field. We then consider their associated gradient flows and, using a gauge fixing technique, are able to prove short time existence for the flows. We then prove energy estimates along the flow, and establish local L 2 -derivative estimates. These are then used to show long time existence of the flow in sub-critical dimensions. In the critical dimension, we are able to show that long time existence is obstructed by an L k+2 curvature concentration phenomenon.Date: February 26, 2018.

show abstract

Section: Introductionsupporting

confidence: 83%

“…The above theorem can be seen as an analogue of the first part of theorem 7.8 in [10], and theorem A in [8], for the case of these higher order Seiberg-Witten functionals. 8.2.…”

Section: Long Time Existence Resultsmentioning

confidence: 80%

“…Finally, we will need the following interpolation result, see corollary 5.5 in [8], and corollary 5.3 in [9]. Lemma 10.3.…”

Section: Long Time Existence Resultsmentioning

confidence: 99%

Section: Long Time Existence Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Higher order Seiberg–Witten functionals and their associated gradient flows

Saratchandran

2018

manuscripta math.

View full text Add to dashboard Cite

show abstract

Essential self-adjointness of perturbed quadharmonic operators on Riemannian manifolds with an application to the separation problem

Saratchandran¹

2019

Preprint

View full text Add to dashboard Cite

We consider perturbed quadharmonic operators, ∆ 4 + V , acting on sections of a Hermitian vector bundle over a complete Riemannian manifold, with the potential V satisfying a bound from below by a non-positive function depending on the distance from a point. Under a bounded geometry assumption on the Hermitian vector bundle and the underlying Riemannian manifold, we give a sufficient condition for the essential self-adjointness of such operators. We then apply this to prove the separation property in L 2 when the perturbed operator acts on functions. Contents 1. Introduction 2.2. Bounded Geometry 2.3. Cut-off functions 2.4. Commutation formulae for connections 3. Main results 4. Localised covariant derivative estimates 5. Derivative estimates for powers of cut-off functions 6. Localised Laplacian estimates 7. Proof of theorem 3.1 8. Localised derivative estimates for the magnetic Laplacian 9. Proof of theorem 3.2 10. Application to the separation problem: Proof of corollary 3.3 11. Concluding remarks: The case of higher order even perturbations References

show abstract

Higher order Yang-Mills flow

Cited by 2 publications

References 0 publications

Higher order Seiberg–Witten functionals and their associated gradient flows

Higher order Seiberg–Witten functionals and their associated gradient flows

Essential self-adjointness of perturbed quadharmonic operators on Riemannian manifolds with an application to the separation problem

Contact Info

Product

Resources

About