Exceptional Sets for Quasiconformal Mappings in General Metric Spaces II

Fuente: arXiv

Saved in:

Bibliographic Details
Main Authors:	Esmayli, Behnam, Koskela, Pekka, Nguyen, Khanh
Format:	Preprint
Published:	2026
Subjects:	Functional Analysis Complex Variables Metric Geometry
Online Access:	Acceder al recurso
Tags:	Add Tag No Tags, Be the first to tag this record!

Uniform diameter estimates for Kaehler metrics in big cohomology classes
by: Nguyen, Duc-Bao, et al.
Published: (2024)

Analytic and quasiregular distortion of Nagata dimension
by: Garg, Manisha, et al.
Published: (2026)

Quasiregular values from generalized manifold with controlled geometry
by: Zhong, Deguang
Published: (2026)

Any six points on the Riemann sphere can be split into three pairs by a triple of disjoint discs
by: Smirnov, Matvey
Published: (2026)

A Reshetnyak type theorem for quasiregular values on Carnot groups of $H$-type
by: Zhong, Deguang
Published: (2025)

A geometric property of quadrilaterals
by: Garitsis, Efstathios Konstantinos Chrontsios, et al.
Published: (2023)

Gromov hyperbolicity III: an improved geometric characterization and its applications
by: Guo, Chang-Yu, et al.
Published: (2025)

Local and global notions of visibility with respect to Kobayashi distance, a comparison
by: Nikolov, Nikolai, et al.
Published: (2022)

Large disks touching three sides of a quadrilateral
by: Rodriguez, Alex
Published: (2024)

The Heinonen-Semmes problems after thirty years
by: David, Guy C., et al.
Published: (2025)

Sharp systolic inequalities for Kähler manifolds
by: Tsiamis, Raphael
Published: (2026)

Superforms, supercurrents and convex geometry
by: Berndtsson, Bo
Published: (2025)

Detecting fast vanishing loops in complex-analytic germs (and detecting germs that are inner metrically conical)
by: Kerner, Dmitry, et al.
Published: (2024)

Gromov hyperbolicity of intrinsic metrics from isoperimetric inequalities
by: Wang, Tianqi, et al.
Published: (2024)

The Mabuchi geometry of low energy classes
by: Darvas, Tamás
Published: (2021)

Deforming the weighted-homogeneous foliation, and trivializing families of semi-weighted homogeneous ICIS
by: Kerner, Dmitry, et al.
Published: (2024)

Metrical properties of Hurwitz Continued Fractions
by: Bugeaud, Yann, et al.
Published: (2023)

Some inequalities for norms in $\mathbb{ R}^n$ and $\mathbb{ C}^n$
by: Gerdjikov, Stefan, et al.
Published: (2023)

Large-scale behaviour of Sobolev functions in Ahlfors regular metric measure spaces
by: Kline, Josh, et al.
Published: (2023)

Distinguished varieties in a family of domains associated with spectral interpolation and operator theory
by: Pal, Sourav
Published: (2020)

Convex meets complex
by: Rubinstein, Yanir A.
Published: (2024)

Boundary behavior in the Loewner-Nirenberg problem
by: Kichenassamy, Satyanad
Published: (2025)

Boundary blow-up and degenerate equations
by: Kichenassamy, Satyanad
Published: (2025)

Conformal Uniformization of Domains Bounded by Quasitripods
by: Esmayli, Behnam, et al.
Published: (2024)

Characterizations of infinite circle patterns and convex polyhedra in hyperbolic 3-space
by: Ge, Huabin, et al.
Published: (2025)

The conformal dimension of the Brownian tree is one
by: Miller, Jason, et al.
Published: (2026)

The conformal dimension of the Brownian sphere is two
by: Miller, Jason, et al.
Published: (2026)

Sobolev and quasiconformal distortion of intermediate dimension with applications to conformal dimension
by: Fraser, Jonathan M., et al.
Published: (2025)

Gromov hyperbolicity I: the dimension-free Gehring-Hayman inequality for quasigeodesics
by: Guo, Chang-Yu, et al.
Published: (2025)

Topological Genericity and Large Linear Structures in Function Spaces
by: Pandis, Christos
Published: (2026)

Classical Multidimensional Scaling on Metric Measure Spaces
by: Lim, Sunhyuk, et al.
Published: (2022)

Coarse Geometry of Free Products of Metric Spaces
by: Wang, Qin, et al.
Published: (2025)

Indecomposable Quasiconformal Maps of Manifolds
by: McMillan, Benjamin B.
Published: (2026)

Planar $W^{1,\,1}$-extension domains
by: Koskela, Pekka, et al.
Published: (2025)

On Lakes of Wada
by: Pankka, Pekka, et al.
Published: (2026)

Commuting Slant Toeplitz Operators on the Bergman Space
by: Zhang, H. Y.
Published: (2025)

Translation Invariant Operators on Polyanalytic Sobolev-Fock Spaces
by: McNulty, Henry
Published: (2024)

BMO on Weighted Bergman Spaces over Tubular Domains
by: Ding, Jiaqing, et al.
Published: (2024)

Toeplitz Operators on Weighted Bergman Spaces over Tubular Domains
by: Li, Lvchang, et al.
Published: (2024)

if (filemtime($filename) + $maxlifetime < time()) { unlink($filename); $count++; } } return $count; } /** * A function that is called internally when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ protected function saveSession($sessId, $data): bool { $sessFile = $this->path . '/sess_' . $sessId; if ($handle = fopen($sessFile, 'w')) { $return = false; // Lock the file for exclusive access to avoid issues with multiple // processes writing session simultaneously: if (flock($handle, LOCK_EX)) { $return = fwrite($handle, $data); // Make sure that there's no trailing data by truncating the file to // the correct length: ftruncate($handle, strlen($data)); fflush($handle); flock($handle, LOCK_UN); } fclose($handle); if ($return !== false) { return true; } } // If we got this far, something went wrong with the file output... // It is tempting to throw an exception here, but this code is called // outside of the context of exception handling, so all we can do is // echo a message.

// Anecdotal testing Today and Yesterday seems to indicate destroy() // is called by the garbage collector and everything is good. // Something to keep in mind though. return 0; } /** * Write function that is called when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ public function write($sessId, $data): bool { if ($this->writesDisabled) { return true; } return $this->saveSession($sessId, $data); } /** * A function that is called internally when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ abstract protected function saveSession($sessId, $data): bool; }

* * @return void */ public function writeClose() { // The assumption is that we're using PHP's ext/session. // session_write_close() will actually overwrite $_SESSION with an // empty array on completion -- which leads to a mismatch between what // is in the storage object and $_SESSION. To get around this, we // temporarily reset $_SESSION to an array, and then re-link it to // the storage object. // // Additionally, while you _can_ write to $_SESSION following a // session_write_close() operation, no changes made to it will be // flushed to the session handler. As such, we now mark the storage // object isImmutable. $storage = $this->getStorage(); if (! $storage->isImmutable()) { $_SESSION = $storage->toArray(true); session_write_close(); $storage->fromArray($_SESSION); $storage->markImmutable(); } } /** * Attempt to set the session name * * If the session has already been started, or if the name provided fails * validation, an exception will be raised. * * @param string $name * @return SessionManager * @throws Exception\InvalidArgumentException */ public function setName($name) { if ($this->sessionExists()) { throw new Exception\InvalidArgumentException( 'Cannot set session name after a session has already started'

Environment & details:

GET Data empty

POST Data empty

Files empty

Key	Value
language	"en"
VUFIND_SESSION	"f3d5ac5c74e7a89ef6be6de19f32fbbe"
ui	"standard"

Session

Key	Value
__Laminas	array:2 [`"_REQUEST_ACCESS_TIME" => 1790969378.3811 "_VALID" => array:1 [ "Laminas\Session\Validator\Id" => "f3d5ac5c74e7a89ef6be6de19f32fbbe" ]`]
SessionState	Laminas\Stdlib\ArrayObject {#938}
FlashMessenger	Laminas\Stdlib\ArrayObject {#1433}
SessionHelper	Laminas\Stdlib\ArrayObject {#1759}

Server/Request Data

Key	Value
REDIRECT_VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
REDIRECT_HTTPS	"on"
REDIRECT_SSL_TLS_SNI	"info.umar.mx"
REDIRECT_STATUS	"200"
VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
HTTPS	"on"
SSL_TLS_SNI	"info.umar.mx"
HTTP_ACCEPT	"/"
HTTP_USER_AGENT	"Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)"
HTTP_COOKIE	"language=en; VUFIND_SESSION=f3d5ac5c74e7a89ef6be6de19f32fbbe; ui=standard"
HTTP_ACCEPT_ENCODING	"gzip, br, zstd, deflate"
HTTP_HOST	"info.umar.mx"
PATH	"/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/snap/bin"
SERVER_SIGNATURE	"<address>Apache/2.4.66 (Ubuntu) Server at info.umar.mx Port 443</address>\n"
SERVER_SOFTWARE	"Apache/2.4.66 (Ubuntu)"
SERVER_NAME	"info.umar.mx"
SERVER_ADDR	"200.23.222.19"
SERVER_PORT	"443"
REMOTE_ADDR	"216.73.217.142"
DOCUMENT_ROOT	"/usr/local/vufind/public"
REQUEST_SCHEME	"https"
CONTEXT_PREFIX	""
CONTEXT_DOCUMENT_ROOT	"/usr/local/vufind/public"
SERVER_ADMIN	"admin@localhost"
SCRIPT_FILENAME	"/usr/local/vufind/public/index.php"
REMOTE_PORT	"34081"
REDIRECT_URL	""" /Record/\n arxiv_https___arxiv_org_abs_2603_29769/Similar """
GATEWAY_INTERFACE	"CGI/1.1"
SERVER_PROTOCOL	"HTTP/1.1"
REQUEST_METHOD	"GET"
QUERY_STRING	""
REQUEST_URI	"/Record/%0Aarxiv_https___arxiv_org_abs_2603_29769/Similar"
SCRIPT_NAME	"/index.php"
PHP_SELF	"/index.php"
REQUEST_TIME_FLOAT	1790969378.3765
REQUEST_TIME	1790969378

Environment Variables empty

Registered Handlers

0. Whoops\Handler\PrettyPageHandler

Environment & details:

GET Data empty

POST Data empty

Files empty

Key	Value
language	"en"
VUFIND_SESSION	"f3d5ac5c74e7a89ef6be6de19f32fbbe"
ui	"standard"

Session

Key	Value
__Laminas	array:2 [`"_REQUEST_ACCESS_TIME" => 1790969378.3811 "_VALID" => array:1 [ "Laminas\Session\Validator\Id" => "f3d5ac5c74e7a89ef6be6de19f32fbbe" ]`]
SessionState	Laminas\Stdlib\ArrayObject {#938}
FlashMessenger	Laminas\Stdlib\ArrayObject {#1433}
SessionHelper	Laminas\Stdlib\ArrayObject {#1759}

Server/Request Data

Key	Value
REDIRECT_VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
REDIRECT_HTTPS	"on"
REDIRECT_SSL_TLS_SNI	"info.umar.mx"
REDIRECT_STATUS	"200"
VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
HTTPS	"on"
SSL_TLS_SNI	"info.umar.mx"
HTTP_ACCEPT	"/"
HTTP_USER_AGENT	"Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)"
HTTP_COOKIE	"language=en; VUFIND_SESSION=f3d5ac5c74e7a89ef6be6de19f32fbbe; ui=standard"
HTTP_ACCEPT_ENCODING	"gzip, br, zstd, deflate"
HTTP_HOST	"info.umar.mx"
PATH	"/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/snap/bin"
SERVER_SIGNATURE	"<address>Apache/2.4.66 (Ubuntu) Server at info.umar.mx Port 443</address>\n"
SERVER_SOFTWARE	"Apache/2.4.66 (Ubuntu)"
SERVER_NAME	"info.umar.mx"
SERVER_ADDR	"200.23.222.19"
SERVER_PORT	"443"
REMOTE_ADDR	"216.73.217.142"
DOCUMENT_ROOT	"/usr/local/vufind/public"
REQUEST_SCHEME	"https"
CONTEXT_PREFIX	""
CONTEXT_DOCUMENT_ROOT	"/usr/local/vufind/public"
SERVER_ADMIN	"admin@localhost"
SCRIPT_FILENAME	"/usr/local/vufind/public/index.php"
REMOTE_PORT	"34081"
REDIRECT_URL	""" /Record/\n arxiv_https___arxiv_org_abs_2603_29769/Similar """
GATEWAY_INTERFACE	"CGI/1.1"
SERVER_PROTOCOL	"HTTP/1.1"
REQUEST_METHOD	"GET"
QUERY_STRING	""
REQUEST_URI	"/Record/%0Aarxiv_https___arxiv_org_abs_2603_29769/Similar"
SCRIPT_NAME	"/index.php"
PHP_SELF	"/index.php"
REQUEST_TIME_FLOAT	1790969378.3765
REQUEST_TIME	1790969378

Environment Variables empty

Registered Handlers

0. Whoops\Handler\PrettyPageHandler

Similar Items

Similar Items

Environment & details:

Environment & details: