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Project Euclid (Hosted at Cornell University Library) (192.979 recursos)
Publicacions Matemàtique
Publicacions Matemàtique
Wehrfritz, B. A. F.
Let $V$ be an arbitrary vector space over some division ring $D$, $\mathbf{L}$ a general series of subspaces of $V$ covering all of $V\backslash \{0\}$ and $S$ the full stability subgroup of $\mathbf{L}$ in $\operatorname{GL}(V)$. We prove that always the set of bounded right Engel elements of $S$ is equal to the $\omega$-th term of the upper central series of $S$ and that the set of right Engel elements of $S$ is frequently equal to the hypercentre of $S$.
Møller, Jesper M.; Scherer, Jérôme
Which spaces look like an $n$-sphere through the eyes of the
$n$-th Postnikov section functor and the $n$-connected cover
functor? The answer is what we call the Postnikov genus of the
$n$-sphere. We define in fact the notion of localization genus for
any homotopical localization functor in the sense of Bousfield and
Dror Farjoun. This includes exotic genus notions related for example
to Neisendorfer localization, or the classical Mislin genus, which
corresponds to rationalization.
Bandara, Lashi
We consider pointwise linear elliptic equations of the form $\mathrm{L}_x u_x = \eta_x$
on a smooth compact manifold where the operators $\mathrm{L}_x$ are in divergence
form with real, bounded, measurable coefficients that vary in the space variable $x$.
We establish $\mathrm{L}^{2}$-continuity of the solutions at $x$ whenever
the coefficients of $\mathrm{L}_x$ are $\mathrm{L}^{\infty}$-continuous at $x$
and the initial datum is $\mathrm{L}^{2}$-continuous at $x$. This is obtained
by reducing the continuity of solutions to a homogeneous Kato square root
problem. As an application, we consider a time evolving family of metrics $\mathrm{g}_t$
that is tangential to the Ricci flow almost-everywhere along geodesics when
starting with a smooth initial metric. Under...
Della Pietra, Francesco; di Blasio, Giuseppina
In this paper we prove existence results and asymptotic behavior for strong
solutions $u\in W^{2,2}_{\operatorname{loc}}(\Omega)$ of the nonlinear elliptic
problem \begin{equation}\label{abstr} \begin{cases} -\Delta_{H}u+H(\nabla
u)^{q}+\lambda u=f&\text{in }\Omega,\\ u\rightarrow +\infty &\text{on
}\partial\Omega, \end{cases}\tag{P} \end{equation} where $H$ is a suitable norm
of $\mathbb R^{n}$, $\Omega\subset\mathbb R^{n}$ is a bounded domain,
$\Delta_{H}$ is the Finsler Laplacian, $1\lt q\le 2$, $\lambda>0$, and $f$ is a
suitable function in $L^{\infty}_{\operatorname{loc}}$. Furthermore, we are
interested in the behavior of the solutions when $\lambda\rightarrow 0^{+}$,
studying the so-called ergodic problem associated to (P). A key role
in order to study the ergodic problem will be played by local gradient estimates
for (P).
Dedieu, T.; Sernesi, E.
We investigate the following question: let $C$ be an integral curve contained in
a smooth complex algebraic surface $X$; is it possible to deform $C$ in $X$ into
a nodal curve while preserving its geometric genus?
¶ We affirmatively answer it in most cases when $X$ is a Del Pezzo or Hirzebruch
surface (this is due to Arbarello and Cornalba, Zariski, and Harris), and in
some cases when $X$ is a $K3$ surface. Partial results are given for all
surfaces with numerically trivial canonical class. We also give various examples
for which the answer is negative.
De Pauw, Thierry
We give an example, in the infinite dimensional separable Hilbert space, of a
purely unrectifiable Borel set with finite nonzero one dimensional Hausdorff
measure, whose projection is nonnegligible in a set of directions which is not
Aronszajn null.
del Rio, Heberto; Santos, Walcy; Simanca, Santiago R.
We consider critical points of the global $L^2$-norm of the second fundamental
form, and of the mean curvature vector of isometric immersions of compact
Riemannian manifolds into a fixed background Riemannian manifold, as functionals
over the space of deformations of the immersion. We prove new gap theorems for
these functionals into hyperbolic manifolds, and show that the celebrated gap
theorem for minimal immersions into the standard sphere can be cast as a theorem
about their critical points having constant mean curvature function, and whose
second fundamental form is suitably small in relation to it. In this case, the
various minimal submanifolds that occur at the pointwise upper bound...
Caprau, Carmen and; Urabe, Katherine
We provide a formula for the Dubrovnik polynomial of a rational knot in terms of
the entries of the tuple associated with a braid-form diagram of the knot. Our
calculations can be easily carried out using a computer algebra system.
Hajłasz, Piotr; Liu, Zhuomin
In this paper we present a new characterization of the Sobolev space $W^{1,p}$,
$1\lt p\lt \infty$ which is a higher dimensional version of a result of Waterman
[32]. We also provide a new and simplified proof of a recent result of Alabern,
Mateu, and Verdera [2]. Finally, we generalize the results to the case of
weighted Sobolev spaces with respect to a Muckenhoupt weight.
Hernández, Jesús Hernández; Valdez, Ferrán
Let $S$ be an orientable surface of infinite genus with a finite number of
boundary components. In this work we consider the curve complex
$\mathcal{C}(S)$, the nonseparating curve complex $\mathcal{N}(S)$, and the
Schmutz graph $\mathcal{G}(S)$ of $S$. When all topological ends of $S$ carry
genus, we show that all elements in the automorphism groups
$\operatorname{Aut}(\mathcal{C}(S))$, $\operatorname{Aut}(\mathcal{N}(S))$, and
$\operatorname{Aut}(\mathcal{G}(S))$ are geometric, i.e., these groups
are naturally isomorphic to the extended mapping class group
$\operatorname{MCG}^{*}(S)$ of the infinite surface $S$. Finally, we study
rigidity phenomena within $\operatorname{Aut}(\mathcal{C}(S))$ and
$\operatorname{Aut}(\mathcal{N}(S))$.
Křepela, Martin
We characterize the validity of the bilinear Hardy inequality for nonincreasing
functions \[ \|f^{**} g^{**}\|_{L^q(w)} \le C
\|f\|_{\Lambda^{p_1}(v_1)}\|g\|_{\Lambda^{p_2}(v_2)}, \] in terms of the weights
$v_1$, $v_2$, $w$, covering the complete range of exponents $p_1,p_2,q\in
(0,\infty]$. The problem is solved by reducing it into the iterated Hardy-type
inequalities \begin{align*} \left( \int\limits_0^\infty \biggl( \int\limits_0^x
(g^{**}(t))^\alpha \varphi(t)\,\mathrm{d}t \biggr)^\frac{\beta}{\alpha}
\psi(x)\,\mathrm{d}x \right)^\frac{1}{\beta} & \le C \biggl(
\int\limits_0^\infty (g^*(x))^\gamma \omega(x) \,\mathrm{d}x
\biggr)^\frac{1}{\gamma}, \\ \left( \int\limits_0^\infty \biggl(
\int\limits_x^\infty (g^{**}(t))^\alpha \varphi(t)\,\mathrm{d}t
\biggr)^\frac{\beta}{\alpha} \psi(x)\,\mathrm{d}x \right)^\frac{1}{\beta} &
\le C \biggl( \int\limits_0^\infty (g^*(x))^\gamma \omega(x) \,\mathrm{d}x
\biggr)^\frac{1}{\gamma}. \end{align*} Validity of these inequalities is
characterized here for $0\lt\alpha\le\beta\lt\infty$ and
$0\lt\gamma\lt\infty$.
Hosseini, Maliheh; Sady, Fereshteh
Let $X$, $Y$ be Hausdorff topological spaces, and let $E$ and $F$ be Hausdorff
topological vector spaces. For certain subspaces $A(X, E)$ and $A(Y,F)$ of
$C(X,E)$ and $C(Y,F)$ respectively (including the spaces of Lipschitz
functions), we characterize surjections $S,T\colon A(X,E) \rightarrow A(Y,F)$,
not assumed to be linear, which jointly preserve common zeros in the sense that
$Z(f-f') \cap Z(g-g') \neq \emptyset$ if and only if $Z(Sf-Sf') \cap Z(Tg-Tg')
\neq \emptyset$ for all $f,f',g,g'\in A(X,E)$. Here $Z(\cdot)$ denotes the zero
set of a function. Using the notion of point multipliers we extend the notion of
zero set for the elements of a Banach module and give a representation for
surjective...
Brown, Lawrence G.
The main result (roughly) is that if $(H_i)$ converges weakly to $H$ and if also
$f(H_i)$ converges weakly to $f(H)$, for a single strictly convex continuous
function $f$, then $(H_i)$ must converge strongly to $H$. One application is
that if $f({\operatorname{pr}}(H))={\operatorname{pr}} (f(H))$, where
${\operatorname{pr}}$ denotes compression to a closed subspace $M$, then $M$
must be invariant for $H$. A consequence of this is the verification of a
conjecture of Arveson, that Theorem 9.4 of [Arv] remains true in the infinite
dimensional case. And there are two applications to operator algebras. If $h$
and $f(h)$ are both quasimultipliers, then $h$ must be a multiplier. Also (still
roughly stated), if $h$...
Ferreira, Lucas C. F.; Lima, Lidiane S. M.
We consider a family of dissipative active scalar equations outside the
$L^{2}$-space. This was introduced in [7] and its velocity fields are coupled
with the active scalar via a class of multiplier operators which morally behave
as derivatives of positive order. We prove global well-posedness and time-decay
of solutions, without smallness assumptions, for initial data belonging to the
critical Lebesgue space $L^{\frac{n}{2\gamma-\beta}}(\mathbb{R}^{n})$ which is a
class larger than that of the above reference. Symmetry properties of solutions
are investigated depending on the symmetry of initial data and coupling
operators.
Belk, James; Matucci, Francesco
We prove that Claas Röver's Thompson-Grigorchuk simple group $V\mathcal{G}$ has
type $F_\infty$. The proof involves constructing two complexes on which
$V\mathcal{G}$ acts: a simplicial complex analogous to the Stein complex for
$V$, and a polysimplicial complex analogous to the Farley complex for $V$. We
then analyze the descending links of the polysimplicial complex, using a theorem
of Belk and Forrest to prove increasing connectivity.
Zhao, Weiren; Wang, Meng; Zhao, Guoping
We consider the integral domain restriction operator $T_{\Omega}$ for certain
bilinear operator $T$. We obtain that if $(s,p_1,p_2)$ satisfies
$\frac{1}{p_1}+\frac{1}{p_2}\geq \frac{2}{\min\{1,s\}}$ and
$\|T\|_{L^{p_1}\times L^{p_2}\rightarrow L^s}\lt\infty$, then
$\|T_{\Omega}\|_{L^{p_1}\times L^{p_2}\rightarrow L^s}\lt\infty$. For some
special domain $\Omega$, this property holds for triplets $(s,p_1,p_2)$
satisfying $\frac{1}{p_1}+\frac{1}{p_2}\gt\frac{1}{\min\{1,s\}}$.
Egert, Moritz; Haller-Dintelmann, Robert; Tolksdorf, Patrick
On a domain $\Omega \subseteq \mathbb{R}^d$ we consider second-order elliptic
systems in divergence-form with bounded complex coefficients, realized via a
sesquilinear form with domain $\mathrm{H}_0^1(\Omega) \subseteq \mathcal{V}
\subseteq \mathrm{H}^1(\Omega)$. Under very mild assumptions on~$\Omega$ and
$\mathcal{V}$ we show that the solution to the Kato Square Root Problem for such
systems can be deduced from a regularity result for the fractional powers of the
negative Laplacian in the same geometric setting. This extends earlier results
of McIntosh [25] and Axelsson-Keith-McIntosh [6] to non-smooth coefficients and
domains.
David, G.
We prove a monotonicity formula for minimal or almost minimal sets for the
Hausdorff measure $\mathcal H^d$, subject to a sliding boundary constraint where
competitors for $E$ are obtained by deforming $E$ by a one-parameter family of
functions $\varphi_t$ such that $\varphi_t(x) \in L$ when $x\in E$ lies on the
boundary $L$. In the simple case when $L$ is an affine subspace of dimension
$d-1$, the monotone or almost monotone functional is given by $F(r) = r^{-d}
\mathcal H^d(E \cap B(x,r)) + r^{-d} \mathcal H^d(S \cap B(x,r))$, where $x$ is
any point of $E$ (not necessarily on $L$) and $S$ is the shade of $L$ with a
light...
Dieu, Nguyen Quang; Manh, Phung Van; Bang, Pham Hien; Hung, Le Thanh
Let $\{f_m\}_{m \ge 1}$ be a sequence of holomorphic functions defined on a
bounded domain $D \subset \mathbb C^n$ or a sequence of rational functions $(1
\le \deg r_m \le m)$ defined on $\mathbb C^n$. We are interested in finding
sufficient conditions to ensure the convergence of $\{f_m\}_{m \ge 1}$ on a
large set provided the convergence holds pointwise on a not too small set. This
type of result is inspired from a theorem of Vitali which gives a positive
answer for uniformly bounded sequence.
Dimant, Verónica; Sevilla-Peris, Pablo
We investigate the summability of the coefficients of $m$-homogeneous polynomials
and $m$-linear mappings defined on $\ell_{p}$ spaces. In our research we obtain
results on the summability of the coefficients of $m$-linear mappings defined on
$\ell_{p_{1}} \times \dotsb \times \ell_{p_{m}}$. The first results in this
respect go back to Littlewood [17] and Bohnenblust and [6] for bilinear and
$m$-linear forms on $c_{0}$, and Hardy and Littlewood [15] and Praciano-Pereira
[20] for bilinear and $m$-linear forms on arbitrary $\ell_{p}$ spaces. Our
results recover and in some case complete these old results through a general
approach on vector valued $m$-linear mappings.