Envoi de contenu de formulaire par mail

Bonjour,

J'ai beau re-verifier mon code, je ne vois pas d'ou viens l'erreur...
En fait tout fonctionne sauf l'envoi du mail a la fin.

<?
if (empty($name))
{
echo ("Please, enter your name. Thank You");
exit();
}
if (empty($email))
{
echo ("Please, enter your email. Thank You");
exit();
}
if (empty($subject))
{
echo ("Please, enter a subject. Thank You");
exit();
}
if (empty($message))
{
echo ("Please, enter a message. Thank you");
exit();
}
if (isset($_POST['name']) AND isset($_POST['email']) AND isset($_POST['subject']) AND isset($_POST['message']))
{
$name = ($_POST['name']);
$email = ($_POST['email']);
$subject = ($_POST['subject']);
$message = ($_POST['message']);

$recipient = "PersonWhoGetsIt@sendesa.com"; //recipient
$header = "From: ". $name . " <" . $email . ">\r\n"; //optional headerfields
}

$mail_sent = @mail($recipient, $subject, $message, $header); //mail command :)
echo $mail_sent ? "Mail sent" : "Mail failed";

?>