monotonicity
Differences
This shows you the differences between two versions of the page.
| Both sides previous revisionPrevious revision | |||
| monotonicity [2023/06/07 13:07] – spencer | monotonicity [2023/06/07 13:12] (current) – [Bellettini-Tian almost-monotonicity] spencer | ||
|---|---|---|---|
| Line 31: | Line 31: | ||
| ==== Bellettini-Tian almost-monotonicity ==== | ==== Bellettini-Tian almost-monotonicity ==== | ||
| - | This almost-monotonicity formula is for triholomorphic maps on hyperkahler manifolds; that is, maps $u \colon (M, I_1, I_2, I_3) \to (N, J_1, J_2, J_3)$ of hyperkahler manifolds that satisfy the triholomorphic map equation | + | This almost-monotonicity formula is for triholomorphic maps on hyperkahler manifolds; that is, maps $u \colon (M^m, I_1, I_2, I_3) \to (N^n, J_1, J_2, J_3)$ of hyperkahler manifolds that satisfy the triholomorphic map equation |
| $$du = \sum_{i=1}^3 J_i du I_i.$$ | $$du = \sum_{i=1}^3 J_i du I_i.$$ | ||
| + | Triholomorphic maps enjoy monotonicity of the form $r^{2-m} \int_{B_r} |\nabla u|^2 = f(r) + O(r f(r))$ where $f$ is a non-decreasing function of $r$. | ||
| ==== Walpuski almost-monotonicity ==== | ==== Walpuski almost-monotonicity ==== | ||
monotonicity.1686157663.txt.gz · Last modified: by spencer