
Softcover ISBN: | 978-2-85629-961-6 |
Product Code: | AST/436 |
List Price: | $57.00 |
AMS Member Price: | $45.60 |

Softcover ISBN: | 978-2-85629-961-6 |
Product Code: | AST/436 |
List Price: | $57.00 |
AMS Member Price: | $45.60 |
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Book DetailsAstérisqueVolume: 436; 2022; 132 ppMSC: Primary 35; 70
This is the first part of the four-paper sequence which establishes the Threshold Conjecture and the Soliton Bubbling vs. Scattering Dichotomy for the energy critical hyperbolic Yang-Mills equation in the \((4 + 1)\)-dimensional Minkowski space-time.
The primary subject of this paper, however, is another PDE, namely the energy critical Yang-Mills heat flow on the 4-dimensional Euclidean space. The authors' first goal is to establish sharp criteria for global existence and asymptotic convergence to a flat connection for this system in \(\dot{H}^{1}\), including the Dichotomy Theorem (i.e., either the above properties hold or a harmonic Yang-Mills connection bubbles off) and the Threshold Theorem (i.e., if the initial energy is less than twice that of the ground state, then the above properties hold). The authors' second goal is to use the Yang-Mills heat flow in order to define the caloric gauge which will play a major role in the analysis of the hyperbolic Yang-Mills equation in the subsequent papers.
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
ReadershipGraduate students and research mathematicians.
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This is the first part of the four-paper sequence which establishes the Threshold Conjecture and the Soliton Bubbling vs. Scattering Dichotomy for the energy critical hyperbolic Yang-Mills equation in the \((4 + 1)\)-dimensional Minkowski space-time.
The primary subject of this paper, however, is another PDE, namely the energy critical Yang-Mills heat flow on the 4-dimensional Euclidean space. The authors' first goal is to establish sharp criteria for global existence and asymptotic convergence to a flat connection for this system in \(\dot{H}^{1}\), including the Dichotomy Theorem (i.e., either the above properties hold or a harmonic Yang-Mills connection bubbles off) and the Threshold Theorem (i.e., if the initial energy is less than twice that of the ground state, then the above properties hold). The authors' second goal is to use the Yang-Mills heat flow in order to define the caloric gauge which will play a major role in the analysis of the hyperbolic Yang-Mills equation in the subsequent papers.
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
Graduate students and research mathematicians.