Shrinkers of the area-preserving curve-shortening flow: Existence and saddle-point property

Fuente: arXiv

Salvato in:

Dettagli Bibliografici
Autore principale:	Cernomazov, Nikita
Natura:	Preprint
Pubblicazione:	2025
Soggetti:	Differential Geometry
Accesso online:	Acceder al recurso
Tags:	Aggiungi Tag Nessun Tag, puoi essere il primo ad aggiungerne!!

Documenti analoghi

Lectures on curve shortening flow
di: Haslhofer, Robert
Pubblicazione: (2026)

Classification of ancient finite-entropy curve shortening flows
di: Choi, Kyeongsu, et al.
Pubblicazione: (2026)

Ancient curve shortening flow in the disc with mixed boundary condition
di: Langford, Mat, et al.
Pubblicazione: (2024)

On bounds of entropy and total curvature for ancient curve shortening flows
di: Su, Wei-Bo, et al.
Pubblicazione: (2024)

Uniqueness of tangent flows at infinity for finite-entropy shortening curves
di: Choi, Kyeongsu, et al.
Pubblicazione: (2024)

Geometric Structure of Ends of Ricci Shrinkers
di: Bertellotti, Alessandro, et al.
Pubblicazione: (2025)

K-polystability of Asymptotically Conical Kähler-Ricci Shrinkers
di: Cifarelli, Charles, et al.
Pubblicazione: (2025)

Geometric aspects of the curve shortening flow in the hyperbolic plane
di: Krznarić, Ivan, et al.
Pubblicazione: (2026)

Rigidity Results for Spacelike Self-Shrinkers via Different Maximum Principles
di: Barboza, Weiller F. Chaves
Pubblicazione: (2025)

On length-preserving and area-preserving inverse curvature flows in the hyperbolic plane
di: Liu, Zhishuai, et al.
Pubblicazione: (2026)

Singular Kähler-Ricci Shrinkers are Complex Analytic
di: Hallgren, Max, et al.
Pubblicazione: (2026)

Semi-Continuity of the Morse Index for Ricci Shrinkers
di: Yudowitz, Louis
Pubblicazione: (2024)

Generating Shrinkers by Mean Curvature Flow
di: Hoffman, David, et al.
Pubblicazione: (2025)

Curve shortening flows on surfaces that are not convex at infinity
di: Fujihara, Naotoshi
Pubblicazione: (2024)

On length-preserving and area-preserving inverse curvature flow of planar curves with singularities
di: Yang, Yunlong, et al.
Pubblicazione: (2024)

Curve shortening flow on Riemann surfaces with conical singularities
di: Roidos, Nikolaos, et al.
Pubblicazione: (2020)

Convergence of the inverse Monge-Ampere flow and Nadel multiplier ideal sheaves
di: Klemyatin, Nikita
Pubblicazione: (2024)

Curve shortening flow with an ambient force field
di: Cuthbertson, Sam, et al.
Pubblicazione: (2024)

Existence of twisted Calabi flow and deformation from the $J$-flow to Calabi flow
di: He, Jie, et al.
Pubblicazione: (2025)

Existence and applications of Ricci flows via pseudolocality
di: He, Fei
Pubblicazione: (2016)

Rigidity and Classification of Legendrian Self-Shrinkers
di: Chang, Shu-Cheng, et al.
Pubblicazione: (2025)

Monotonicity of the modulus under curve shortening flow
di: Sobnack, Arjun, et al.
Pubblicazione: (2024)

Existence and stability of weak critical points of $r$-energy functionals
di: Montaldo, Stefano, et al.
Pubblicazione: (2026)

On a non-local area-preserving curve flow
di: Sun, Zezhen, et al.
Pubblicazione: (2025)

On an area-preserving inverse curvature flow for plane curves
di: Sun, Zezhen, et al.
Pubblicazione: (2025)

Eigenvalue Estimates for Schrödinger Operators on Ricci Shrinkers
di: Cheng, Xu, et al.
Pubblicazione: (2026)

Existence and convergence of the length-preserving elastic flow of clamped curves
di: Rupp, Fabian, et al.
Pubblicazione: (2020)

Noncommutative rigidity of the moduli stack of stable pointed curves
di: Okawa, Shinnosuke, et al.
Pubblicazione: (2014)

From curve shortening to flat link stability and Birkhoff sections of geodesic flows
di: Alves, Marcelo R. R., et al.
Pubblicazione: (2024)

Stability of the surface diffusion flow and volume-preserving mean curvature flow in the flat torus
di: De Gennaro, Daniele, et al.
Pubblicazione: (2023)

Closed Ricci Flows with Singularities Modeled on Asymptotically Conical Shrinkers
di: Stolarski, Maxwell
Pubblicazione: (2022)

The asymptotic of the Mullins-Sekerka and the area-preserving curvature flow in the planar flat torus
di: Arya, Vedansh, et al.
Pubblicazione: (2025)

Constructing $λ$-Angenent curve by flow method
di: Ho, Pak Tung
Pubblicazione: (2026)

Delayed parabolic regularity for curve shortening flow
di: Sobnack, Arjun, et al.
Pubblicazione: (2024)

The behaviour of moving points on curves: A rotating frame approach
di: Han, Dong
Pubblicazione: (2026)

The inverse curve shortening flow on the hyperbolic plane
di: Krznarić, Ivan, et al.
Pubblicazione: (2026)

Legendrian curve flow in Sasakian sub-Riemannian 3-manifolds
di: Cui, Jingshi, et al.
Pubblicazione: (2025)

Positive sectional curvature is not preserved under the Ricci flow in dimensions seven and thirteen
di: González-Álvaro, David, et al.
Pubblicazione: (2024)

Bounds on saddle connections for flat spheres
di: Fu, Kai, et al.
Pubblicazione: (2023)

Existence and partial regularity of Legendrian area-minimizing currents
di: Orriols, Gerard
Pubblicazione: (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
VUFIND_SESSION	"b234f20e6498436b5ec04bbada9a12e5"
ui	"standard"
language	"it"

Session

Key	Value
__Laminas	array:2 [`"_REQUEST_ACCESS_TIME" => 1790863271.6156 "_VALID" => array:1 [ "Laminas\Session\Validator\Id" => "b234f20e6498436b5ec04bbada9a12e5" ]`]
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	"VUFIND_SESSION=b234f20e6498436b5ec04bbada9a12e5; ui=standard; language=it"
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	"216.73.216.147"
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	"40884"
REDIRECT_URL	""" /Record/\n arxiv_https___arxiv_org_abs_2508_00352/Similar """
GATEWAY_INTERFACE	"CGI/1.1"
SERVER_PROTOCOL	"HTTP/1.1"
REQUEST_METHOD	"GET"
QUERY_STRING	""
REQUEST_URI	"/Record/%0Aarxiv_https___arxiv_org_abs_2508_00352/Similar"
SCRIPT_NAME	"/index.php"
PHP_SELF	"/index.php"
REQUEST_TIME_FLOAT	1790863271.6113
REQUEST_TIME	1790863271

Environment Variables empty

Registered Handlers

0. Whoops\Handler\PrettyPageHandler