اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدSecond order rectifiability of integral varifolds of locally bounded first variation
110
0
0.0
(
0
)
تأليف
Ulrich Menne
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
In this work it is shown that every integral varifold in an open subset of Euclidian space of locally bounded first variation can be covered by a countable collection of submanifolds of class C^2. Moreover, the mean curvature of each member of the collection agrees with the mean curvature of the varifold almost everywhere with respect to the varifold.
قيم البحث
اقرأ أيضاً
In this work the Isoperimetric Inequality for integral varifolds is used to obtain sharp estimates for the size of the set where the density quotient is small and to generalise Calderons and Zygmunds theory of first order differentiability for functi
ons in Lebesgue spaces from Lebesgue measure to integral varifolds.
We study the asymptotics as $puparrow 2$ of stationary $p$-harmonic maps $u_pin W^{1,p}(M,S^1)$ from a compact manifold $M^n$ to $S^1$, satisfying the natural energy growth condition $$int_M|du_p|^p=O(frac{1}{2-p}).$$ Along a subsequence $p_jto 2$, w
e show that the singular sets $Sing(u_{p_j})$ converge to the support of a stationary, rectifiable $(n-2)$-varifold $V$ of density $Theta_{n-2}(|V|,cdot)geq 2pi$, given by the concentrated part of the measure $$mu=lim_{jtoinfty}(2-p_j)|du_{p_j}|^{p_j}dv_g.$$ When $n=2$, we show moreover that the density of $|V|$ takes values in $2pimathbb{N}$. Finally, on every compact manifold of dimension $ngeq 2$ we produce examples of nontrivial families $(1,2) i pmapsto u_pin W^{1,p}(M,S^1)$ of such maps via natural min-max constructions.
We give various estimates of the first eigenvalue of the $p$-Laplace operator on closed Riemannian manifold with integral curvature conditions.
The conformal parameterisation of a minimal surface is harmonic. Therefore, a minimal surface is a critical point of both the energy functional and the area functional. In this paper, we compare the Morse index of a minimal surface as a critical poin
t of the area functional with its Morse index as a critical point of the energy functional. The difference between these indices is at most the real dimension of Teichmuller space. This comparison allows us to obtain surprisingly good upper bounds on the index of minimal surfaces of finite total curvature in Euclidean space of any dimension. We also bound the index of a minimal surface in an arbitrary Riemannian manifold by the area and genus of the surface, and the dimension and geometry of the ambient manifold.
In this paper we prove convergence and compactness results for Ricci flows with bounded scalar curvature and entropy. More specifically, we show that Ricci flows with bounded scalar curvature converge smoothly away from a singular set of codimension
$geq 4$. We also establish a general form of the Hamilton-Tian Conjecture, which is even true in the Riemannian case. These results are based on a compactness theorem for Ricci flows with bounded scalar curvature, which states that any sequence of such Ricci flows converges, after passing to a subsequence, to a metric space that is smooth away from a set of codimension $geq 4$. In the course of the proof, we will also establish $L^{p < 2}$-curvature bounds on time-slices of such flows.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
