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pro vyhledávání: '"Feehan, Paul M. N."'
Autor:
Feehan, Paul M. N., Leness, Thomas G.
This work is a sequel to our previous monograph arXiv:2010.15789 (to appear in AMS Memoirs), where we initiated our program to prove that the Bogomolov-Miyaoka-Yau inequality holds for closed, symplectic four-manifolds and, more generally, for closed
Externí odkaz:
http://arxiv.org/abs/2410.13809
Autor:
Feehan, Paul M. N.
Our goal in this work is to develop aspects of Bialynicki-Birula and Morse-Bott theory that can be extended from the classical setting of smooth manifolds to that of complex analytic spaces with a holomorphic $\mathbb{C}^*$ action. We extend prior re
Externí odkaz:
http://arxiv.org/abs/2206.14710
Autor:
Feehan, Paul M. N., Leness, Thomas G.
We previously developed an approach to Bialynicki-Birula theory for holomorphic $\mathbb{C}^*$ actions on complex analytic spaces and the concept of virtual Morse-Bott indices for singular critical points of Hamiltonian functions for the induced circ
Externí odkaz:
http://arxiv.org/abs/2010.15789
Autor:
Feehan, Paul M. N., Leness, Thomas G.
We describe a new approach to the problem of constructing gluing parameterizations for open neighborhoods of boundary points of moduli spaces of anti-self-dual connections over closed four-dimensional manifolds. Our approach employs general results f
Externí odkaz:
http://arxiv.org/abs/1910.14580
Autor:
Feehan, Paul M. N.
A result (Corollary 4.3) in an article by Uhlenbeck (1985) asserts that the $W^{1,p}$-distance between the gauge-equivalence class of a connection $A$ and the moduli subspace of flat connections $M(P)$ on a principal $G$-bundle $P$ over a closed Riem
Externí odkaz:
http://arxiv.org/abs/1906.03954
We apply our abstract gradient inequalities developed by the authors in arXiv:1510.03817 to prove Lojasiewicz--Simon gradient inequalities for the harmonic map energy function using Sobolev spaces which impose minimal regularity requirements on maps
Externí odkaz:
http://arxiv.org/abs/1903.01953
On the Morse-Bott property of analytic functions on Banach spaces with Lojasiewicz exponent one half
Autor:
Feehan, Paul M. N.
Publikováno v:
Calculus of Variations and Partial Differential Equations 59 (2020), article no. 87, 50 pages
It is a consequence of the Morse-Bott Lemma on Banach spaces that a smooth Morse-Bott function on an open neighborhood of a critical point in a Banach space obeys a Lojasiewicz gradient inequality with the optimal exponent one half. In this article w
Externí odkaz:
http://arxiv.org/abs/1803.11319
Autor:
Feehan, Paul M. N.
Publikováno v:
Geom. Topol. 23 (2019) 3273-3313
The Lojasiewicz inequalities for real analytic functions on Euclidean space were first proved by Stanislaw Lojasiewicz (1965) using methods of semianalytic and subanalytic sets, arguments later simplified by Bierstone and Milman (1988). In this artic
Externí odkaz:
http://arxiv.org/abs/1708.09775
Autor:
Feehan, Paul M. N.
For any compact Lie group $G$ and closed, smooth Riemannian manifold $(X,g)$ of dimension $d\geq 2$, we extend a result due to Uhlenbeck (1985) that gives existence of a flat connection on a principal $G$-bundle over $X$ supporting a connection with
Externí odkaz:
http://arxiv.org/abs/1706.09349