اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدTeissier problem for nef classes
163
0
0.0
(
0
)
تأليف
Yashan Zhang
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Teissier problem aims to characterize the equality case of Khovanskii-Teissier type inequality for (1,1)-classes on a compact Kahler manifold. When each of the involved (1,1)-classes is assumed to be nef and big, this problem has been solved by the previous works of Boucksom-Favre-Jonsson, Fu-Xiao and Li. In this note, we shall settle the case that the involved (1,1)-classes are just assumed to be nef. By constructing examples, it is shown that our results are optimal. We also extend the results to the case when some of the (1,1)-classes are not necessarily nef.
قيم البحث
اقرأ أيضاً
We introduce natural deformation classes of generalized Kahler structures using the Courant symmetry group. We show that these yield natural extensions of the notions of Kahler class and Kahler cone to generalized Kahler geometry. Lastly we show that
the generalized Kahler-Ricci flow preserves this generalized Kahler cone, and the underlying real Poisson tensor.
The Finiteness Problem is shown to be unsolvable for any sufficiently large class of modular lattices.
In this paper, we study stability and instability problem for type-II partitioning problem. First, we make a complete classification of stable type-II stationary hypersurfaces in a ball in a space form as totally geodesic $n$-balls. Second, for gener
al ambient spaces and convex domains, we give some topological restriction for type-II stable stationary immersed surfaces in two dimension. Third, we give a lower bound for the Morse index for type-II stationary hypersurfaces in terms of their topology.
For non-homotopic maps $u,vin C^{infty}(M,N)$ between closed Riemannian manifolds, we consider the smallest energy level $gamma_p(u,v)$ for which there exist paths $u_tin W^{1,p}(M,N)$ connecting $u_0=u$ to $u_1=v$ with $|du_t|_{L^p}^pleq gamma_p(u,v
)$. When $u$ and $v$ are $(k-2)$-homotopic, work of Hang and Lin shows that $gamma_p(u,v)<infty$ for $pin [1,k)$, and using their construction, one can obtain an estimate of the form $gamma_p(u,v)leq frac{C(u,v)}{k-p}$. When $M$ and $N$ are oriented, and $u$ and $v$ induce different maps on real cohomology in degree $k-1$, we show that the growth $gamma_p(u,v)sim frac{1}{k-p}$ as $pto k$ is sharp, and obtain a lower bound for the coefficient $liminf_{pto k}(k-p)gamma_p(u,v)$ in terms of the min-max masses of certain non-contractible loops in the space of codimension-$k$ integral cycles in $M$. In the process, we establish lower bounds for a related smaller quantity $gamma_p^*(u,v)leqgamma_p(u,v)$, for which there exist critical points $u_pin W^{1,p}(M,N)$ of the $p$-energy functional satisfying $gamma_p^*(u,v)leq |du_p|_{L^p}^pleq gamma_p(u,v).$
We prove the existence of solutions to the asymptotic Plateau problem for hypersurfaces of prescribed mean curvature in Cartan-Hadamard manifolds $N$. More precisely, given a suitable subset $L$ of the asymptotic boundary of $N$ and a suitable functi
on $H$ on $N$, we are able to construct a set of locally finite perimeter whose boundary has generalized mean curvature $H$ provided that $N$ satisfies the so-called strict convexity condition and that its sectional curvatures are bounded from above by a negative constant. We also obtain a multiplicity result in low dimensions.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
