论文标题
变形的Hermitian-yang-米尔斯方程，altivstellensatz和可溶性
The Deformed Hermitian--Yang--Mills Equation, the Positivstellensatz, and the Solvability
论文作者
论文摘要
令$（m，ω）$为复合尺寸四的紧凑连接的kähler歧管，让$ [χ] \ in H^{1,1}（M; \ Mathbb {r}）$中的$ [χ] \。我们证实了Collins-Jacob-Yau [Arxiv：1508.01934]的猜想，证明了变形的Hermitian-yang-mills方程的可溶性，该方程式由以下非线性椭圆方程$ \ sum_ sum_ sum_ {i} {i} \ arctan（λ_i）$ y $ y $ a $ a $ a $ a $ a $ a.对$ω$和$ \hatθ$是拓扑常数。该猜想在[arxiv：1508.01934]中说明，其中他们证明存在超批判性$ c $ -subsondolution或$ c $ -suboslution当$ \hatθ\ in [（（n-2} + {2}/{n}）/{n}/{n}）five prives us f in $ \hatθ\ in [（n-2}/{n}） Hermitian-yang-米尔斯方程。 Collins - Jacob-Yau猜想，当$ \hatθ\ in（（（n-2）π/{2}}，（（n-2） + {2}/{n}）π/{2}）$ n $ n $是流形的复杂尺寸，可以改善其存在定理。在本文中，我们确认他们的猜想是，当复数等于四和$ \hatθ$接近右边的超临界相$π$时，那么存在$ c $ -subsolution的存在就意味着变形的Hermitian-yang-mills方程。
Let $(M, ω)$ be a compact connected Kähler manifold of complex dimension four and let $[χ] \in H^{1,1}(M; \mathbb{R})$. We confirmed the conjecture by Collins--Jacob--Yau [arXiv:1508.01934] of the solvability of the deformed Hermitian--Yang--Mills equation, which is given by the following nonlinear elliptic equation $\sum_{i} \arctan (λ_i) = \hatθ$, where $λ_i$ are the eigenvalues of $χ$ with respect to $ω$ and $\hatθ$ is a topological constant. This conjecture was stated in [arXiv:1508.01934], wherein they proved that the existence of a supercritical $C$-subsolution or the existence of a $C$-suboslution when $\hatθ \in [ ( (n-2) + {2}/{n} ) π/{2}, nπ/2 )$ will give the solvability of the deformed Hermitian--Yang--Mills equation. Collins--Jacob--Yau conjectured that their existence theorem can be improved when $\hatθ \in ( (n-2 ) π/{2}, ( (n-2) + {2}/{n} ) π/{2} )$, where $n$ is the complex dimension of the manifold. In this paper, we confirmed their conjecture that when the complex dimension equals four and $\hatθ$ is close to the supercritical phase $π$ from the right, then the existence of a $C$-subsolution implies the solvability of the deformed Hermitian--Yang--Mills equation.
