Script php per invio email

Salve a tutti sono alle prime armi in php non sto riuscendo a capire perché lo script php all' invio del form mi arriva la mail senza i capi di input.

<section id="feature">
          <div class="wrapper">
          
               <!-- ################################################################################################ -->
               <div class="center btmspace-80">
                 <!-- <h2 class="heading  btmspace-30 reveal" style="color: red; font-size:35px;"><strong>Per qualsiasi informazione Contattaci</strong></h2>
                 <p class="lrspace reveal" style="font-size: 17px;">
                   Informazioni preventivi e gestioni sinistri contattaci tramite il forum e ti risponderemo il prima possibile.
                 </p> -->
           
                 <div class="conta_formu">
                   <h2 class=" big-text" id="title_forum"></h2>
                   <p class="text_forum"> </p>
                   <form action="<?php echo $_SERVER['PHP_SELF'] ?>" method="POST" >
                       <label for="name">Nome:</label>
                       <input type="text" name="name" id="name" required="true">
                       <label for="address">Cognome:</label>
                       <input type="text" name="address" id="subject" required="true">
                       <label for="email">E-mail:</label>
                       <input type="email" name="email" id="email" required="true">
                       <label for="message">Messaggio</label>
                       <textarea name="message" cols="30" rows="10"placeholder="..."></textarea>
                       <input class="zoom" id="invia" type="submit" value="Invia">
                   </form>
               </div>
          </div>
    </section> 
 
<?php
if ($_SERVER['REQUEST_METHOD'] === 'POST')  {
    $field_name = $_POST['name'];
    $field_email = $_POST['email'];
    $field_message = $_POST['message'];
 
    $field_address = $_POST['address'];
 
    $mail_to = 'info@.com';
    $mail_from = 'Email_From_Website';
    $subject = 'Message from visitor '.$field_name;
 
    $body_message = 'From: '.$field_name."\n";
    $body_message .= 'E-mail: '.$field_email."\n";
 
   
    $body_message .= 'Address: '.$field_address."\n";
    $body_message .= 'Message: '.$field_message;
    $headers = 'From: '.$mail_from."\r\n";
    $headers .= 'Reply-To: '.$field_email."\r\n";
    mail($mail_to, $subject, $body_message, $headers);
 
  
}
?>