# Energy gap for Yang–Mills connections, II: Arbitrary closed Riemannian manifolds ☆

@article{Feehan2017EnergyGF, title={Energy gap for Yang–Mills connections, II: Arbitrary closed Riemannian manifolds ☆}, author={Paul M. N. Feehan}, journal={Advances in Mathematics}, year={2017}, volume={312}, pages={547-587} }

## 19 Citations

### Lojasiewicz–Simon gradient inequality on a Sobolev neighborhood of a ﬂat connection

- Mathematics
- 2017

. We prove an L d/ 2 energy gap result for Yang–Mills connections on principal G bundles, P , over arbitrary, closed, Riemannian, smooth manifolds of dimension d ≥ 2. We apply our version of the…

### Optimal Łojasiewicz–Simon inequalities and Morse–Bott Yang–Mills energy functions

- MathematicsAdvances in Calculus of Variations
- 2021

Abstract For any compact Lie group 𝐺 and closed, smooth Riemannian manifold ( X , g ) (X,g) of dimension d ≥ 2 d\geq 2 , we extend a result due to Uhlenbeck (1985) that gives existence of a flat…

### Energy gap for Yang–Mills connections, I: Four-dimensional closed Riemannian manifolds

- Mathematics
- 2016

### The analysis of inhomogeneous Yang–Mills connections on closed Riemannian manifold

- MathematicsJournal of Mathematical Physics
- 2022

In this article, we study a class of connections on a closed Riemannian manifold X of dimensional n > 4, which we call inhomogeneous Yang–Mills connections. Some special cases included Ω-Yang–Mills…

### Discreteness for energies of Yang-Mills connections over four-dimensional manifolds

- Mathematics
- 2015

We generalize our previous results (Theorem 1 and Corollary 2 in arXiv:1412.4114) and Theorem 1 in arXiv:1502.00668) on the existence of an $L^2$-energy gap for Yang-Mills connections over closed…

### Gap theorems in Yang-Mills theory for complete four-dimensional manifolds with a weighted Poincar\'e inequality

- Mathematics
- 2019

This paper provides two gap theorems in Yang-Mills theory for complete four-dimensional manifolds with a weighted Poincar\'e inequality. The results show that given a Yang-Mills connection on a…

### Łojasiewicz–Simon gradient inequalities for coupled Yang–Mills energy functions

- MathematicsMemoirs of the American Mathematical Society
- 2020

In this sequel to arXiv:1510.03817, we apply our abstract Lojasiewicz-Simon gradient inequality to prove Lojasiewicz-Simon gradient inequalities for coupled Yang-Mills energy functions using Sobolev…

### An Energy Gap for Complex Yang-Mills Equations

- Mathematics
- 2016

We use the energy gap result of pure Yang-Mills equation [Feehan P.M.N., Adv. Math. 312 (2017), 547-587, arXiv:1502.00668] to prove another energy gap result of complex Yang-Mills equations…

### The finite time blow-up of the Yang-Mills flow

- Mathematics
- 2021

In this paper, we shall prove that, on a non-flat Riemannian vector bundle over a compact Riemannian manifold, the smooth solution of the Yang-Mills flow will blow up in finite time if the energy of…

## References

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### Optimal Łojasiewicz–Simon inequalities and Morse–Bott Yang–Mills energy functions

- MathematicsAdvances in Calculus of Variations
- 2021

Abstract For any compact Lie group 𝐺 and closed, smooth Riemannian manifold ( X , g ) (X,g) of dimension d ≥ 2 d\geq 2 , we extend a result due to Uhlenbeck (1985) that gives existence of a flat…

### Energy gap for Yang–Mills connections, I: Four-dimensional closed Riemannian manifolds

- Mathematics
- 2016

### Global existence and convergence of smooth solutions to Yang-Mills gradient flow over compact four-manifolds

- Mathematics
- 2014

In this monograph we develop results on global existence and convergence of solutions to the gradient flow equation for the Yang-Mills energy functional on a principal bundle, with compact Lie…

### Global existence and convergence of solutions to gradient systems and applications to Yang-Mills gradient flow

- Mathematics
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In this monograph, we develop results on global existence and convergence of solutions to abstract gradient flows on Banach spaces for a potential function that obeys the Lojasiewicz-Simon gradient…

### Removable singularities for Yang–Mills connections in higher dimensions

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We prove several removable singularity theorems for singular Yang-Mills connections on bundles over Riemannian manifolds of dimensions greater than four. We obtain the local and global removability…

### Energy Gap Phenomena for Yang-Mills Connections

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We consider a vector bundle E over a compact Riemannian manifold M=M, (n ≥ 4), and A is a Yang-Mills connection on E. Then its energy must be bounded from below by some positive constant unless E is…

### The uniqueness of tangent cones for Yang–Mills connections with isolated singularities

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### The Riemannian geometry of the Yang-Mills moduli space

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The moduli space ℳ of self-dual connections over a Riemannian 4-manifold has a natural Riemannian metric, inherited from theL2 metric on the space of connections. We give a formula for the curvature…

### Stability and isolation phenomena for Yang-Mills fields

- Mathematics
- 1981

In this article a series of results concerning Yang-Mills fields over the euclidean sphere and other locally homogeneous spaces are proved using differential geometric methods. One of our main…