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The Yamabe problem
On Witten's proof of the positive energy theorem
This paper gives a mathematically rigorous proof of the positive energy theorem using spinors. This completes and simplifies the original argument presented by Edward Witten. We clarify the geometricExpand
Bubble tree convergence for harmonic maps
Let Σ be a compact Riemann surface. Any sequence fn : Σ — > M of harmonic maps with bounded energy has a "bubble tree limit" consisting of a harmonic map /o : Σ -> M and a tree of bubbles fk : S2 ->Expand
Relative Gromov-Witten invariants
We define relative Gromov-Witten invariants of a symplectic manifold relative to a codimension-two symplectic submanifold. These invariants are the key ingredients in the symplectic sum formula ofExpand
The symplectic sum formula for Gromov–Witten invariants
In the symplectic category there is a 'connect sum' operation that glues symplectic manifolds by identifying neighborhoods of embedded codimension two submanifolds. This paper establishes a formulaExpand
Gauge theories on four dimensional Riemannian manifolds
This paper develops the Riemannian geometry of classical gauge theories — Yang-Mills fields coupled with scalar and spinor fields — on compact four-dimensional manifolds. Some important properties ofExpand
Pseudo-holomorphic maps and bubble trees
This paper proves a strong convergence theorem for sequences of pseudo-holomorphic maps from a Riemann surface to a symplectic manifoldN with tamed almost complex structure. (These are the objectsExpand
Invariants of conformal Laplacians
The conformal Laplacian D = d*d + (n - 2)s/4(n - 1), acting on functions on a Riemannian manifold Mn with scalar curvature s, is a conformally invariant operator. In this paper we will use D toExpand