"In the last several years, the study of gauge theories in quantum field theory has led to some interesting problems in nonlinear elliptic differential equations. One such problem is the local behavior of Yang-Mills fields ... over Euclidean 4-space. Our main result is a local regularity theorem: A Yang-Mills field with finite energy over a 4-manifold cannot have isolated singularities. Apparent point singularities (including singularities in the bundle) can be removed by a gauge transformation. In particular, a Yang-Mills field for a bundle over R4 which has finite energy may be extended to a smooth field over R4 \cup {∞} = S4."
Quote Details
Added by wikiquote-import-bot
Unverified quote
0 likes
People from New JerseyWomen academics from the United StatesNational Medal of Science laureatesScientists from ClevelandAbel Prize laureates
Original Language: English
Available Languages (1)
Sources
Imported from EN Wikiquote
https://en.wikiquote.org/wiki/Karen_Uhlenbeck
Revision History
No revisions have been submitted for this quote.
Categories
Karen Uhlenbeck
3 quotes on TrueQuotesView all quotes by Karen Uhlenbeck →
Related Quotes
"Most explicit information on the eigenfunctions of a Laplace operator on a compact manifold comes from computations w…"
"How did gauge theory appear and become successful in mathematics in the space of a few years? The fundamental mathema…"
"Shatter her beauteous breast ye may; The Spirit of England none can slay! Dash the bomb on the dome of Paul's, — Deem…"
"Comin' in on a wing and a pray'r Comin' in on a wing and a pray'r Tho' there's one motor gone, We can still carry on,…"
"Each person acts on the assumption that more money will bring more happiness; and, indeed, if he does get more money,…"
"There’s a part of me in every I write, whether it’s male or female, because everything has to go through me. Everythi…"
"Success did come to me later, but that was okay, I could feel myself getting better with each story or book. Age does…"
"I’ve always been fascinated with this sense that every single person walking down the street has a whole story. It’s …"
"My great-grandmother would talk about her uncles who served in the Maine Regiment during the Civil War, my great-gran…"
"The past contains many answers, but until we ask the right questions their meaning eludes us."